"New" Way To Solve Quadratic Equations That Everyone Is Talking About

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This is an incredible problem solving technique. It is amazing the method is not commonly taught.
Original sources - Professor Po-Shen Loh explains the method, history, and gives examples in the following articles and videos. They are worth checking out.
www.poshenloh.com/quadratic
www.poshenloh.com/quadraticde...
www.poshenloh.com/quadraticre...
arxiv.org/abs/1910.06709
• A Different Way to Sol...
• Examples: A Different ...
News stories
www.technologyreview.com/s/61...
www.popularmechanics.com/scie...
Similar methods
The Quadratic Formula, Revisited (Girls' Angle Bulletin Oct/Nov 2017)
girlsangle.org/page/bulletin-a...
Quadratic equations taught in Germany
math.stackexchange.com/questi...
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25 июл 2024

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Комментарии : 2,8 тыс.

@MindYourDecisions 4 года назад

Here's a video I posted 4 years ago, when the channel was just starting: The Quadratic Formula - Why Do We Complete The Square? ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-EBbtoFMJvFc.html I was still new to making videos as the channel was just starting. It took so long to do the animations, and I recorded the entire video in a single take so the video is not as polished. So I was overwhelmed by the positive comments, like: "This video should be presented in every high school and middle school algebra class. "

@akashmukherjee2405 4 года назад

Great video and animations. Helpful for my cousin. ♥️ It's easier to remember than Brahmagupta's formula, but one thing, in engineering level, this method will take a hell of a time to solve.... Brahmagupta's formula will help at that moment. Brilliant idea anyways.

@trailokyatripathy4341 4 года назад

Keep the initially assumed values of B and C in the final result and you will come back to the same old quadratic formula

@akashmukherjee2405 4 года назад

@@trailokyatripathy4341 yep.

@vasilisanagnostopoulos5198 4 года назад

MindYourDecisions These come from the vietta formulas . They’ve been known for years 🤷🏼‍♂️

@moeenuddin6756 4 года назад

MindYourDecisions I wish I knew this 2 year ago

@manishameruliya2011 3 года назад

In India (and many other countries) there are three ways to do it: 1. Split the middle term 2. Completeting Square Method 3. Quadratic Formula

@SantoshSahni23 3 года назад

They( American ) just changed our well known Quadratic formula 😅 . For just getting some credit !

@xdgaming952 3 года назад

i think that's world wide

@lakshyasingh1576 3 года назад

Correct

@yasirarafat7654 3 года назад

I hate completing square method

@mrnobody3758 3 года назад

@@yasirarafat7654 it's ez just watch some yt vids

@aczajka74 4 года назад

This is literally a derivation of the quadratic formula

@bramkivenko9912 4 года назад

If you divide out the equation so "a" is 1, then the quadratic solution is: -½b ± sqrt(¼b²-c). The innovation is the normalization of a=1, means you can solve quadratics faster. This is presumably important for timed math competitions.

@nightsky8191 4 года назад

I thought common derivation of the quadratic formula is by completing the square. Of course the two methods are identical but at least I’m new to this

@Felixr2 4 года назад

@@bramkivenko9912 The thing is, in *both cases* you're dividing two numbers by a. The only difference is if you're dividing by a at the start or at the beginning. This isn't any faster.

@bramkivenko9912 4 года назад

@@Felixr2 I understand, but I think a person can perform this faster while less likely to introduce errors. To each his own.

@R_samurai779 4 года назад

It is the other way around

@chilllife5694 4 года назад

Old: chicken produce eggs America's latest: eggs are produced by chicken .

@HKClasher 4 года назад

🤣🤣🤣🤣🤣

@patrickstar9151 4 года назад

In Europe and US our education is not that hard

@fizixx 4 года назад

You know it's a Chinese guy that came up with this, right?

@shahnazwm 3 года назад

😂 🤣 Lmfao... Underrated

@localtitans4166 3 года назад

What does that mean?

@kabochaVA 4 года назад

The whole comment section: This is "new"? Here in Germany/Russia/India/Greece/... we learn it in 8th grade. It's known as the "pq-Formel" / "Viète's theorem" / "Middle Term Split" / "S(um) and P(roduct) method"...

@shyamparihar4071 4 года назад

yup middle term split here in India....we learn it in 8th Standard and then we learn quadratic formula in 10th Standard....as we cannot solve every quadratic equation by middle term split (easily).

@zynade9334 4 года назад

@@shyamparihar4071 how is this the same as "middle term split" method? He literally used that in the starting of the vid followed by the "new" method

@abhi_shek1196 4 года назад

Also here in Nepal

@maratimus 4 года назад

And China

@justinf8091 4 года назад

I’m in Canada and we learnt this in grade 7😂😂

@algc19 4 года назад

This is literally Diophante's method, step by step. "Ancient mathematicians didn't do it like this" well yes they did

@technicalgamers7324 4 года назад

@plaustrarius 4 года назад

Lol tartaglia, Ferrari, cardano, lagrange, they all knew this and did it better honestly hahaha

@daywill8849 4 года назад

Shri dharacharya invented this... Not some diophante guy

@aayushpatra3823 4 года назад

@@daywill8849 They are talking about the new method, not the old one

@phoenix0278 4 года назад

@@daywill8849 hey@Daywill,He do not invented it he discovered it.....AND he is not the only one...😇

@lowlifexysvendetta5894 4 года назад

I have known this formula as the p q formula And yes, I am from Germany

@rishav-singh 4 года назад

Exactly bro

@frodobeutlin1564 4 года назад

Here in Germany we learn it as a quite simple formula in 9th grade. I learned it in 1999 and still teach it that way.

@geniegerny 4 года назад

Yeah actually we learned this before the other formula, but we only used it when there was no coefficient in front of x^2. They didn't tell us we could just facture out the coefficient :(

@NetAndyCz 4 года назад

Same in Czech republic:) p,q as well. And imho it works well only on nice behaving a, so I prefer the standard formula anyway.

@kariminalo979 4 года назад

Sweden too bro, we calle it PQ-formeln just like on Germany.

@sarthakmirani6121 4 года назад

Presh : Mathematicians found a NEW way for solving quadratic equations The Comments : Nope

@gabrielnobrega1428 4 года назад

It ends up being the same thing, except that instead of memorizing a formula, you're memorizing a method that ends up in the same formula

@jamieg2427 4 года назад

Precisely how I feel. I would rather memorize a formula than a bunch of steps. I feel most students I taught this to wouldn't remember the motivation for most of these steps and instead just memorize. It's better to just teach how to derive the quadratic equation, with variables and with numbers.

@ravindrawiguna8681 4 года назад

@@jamieg2427 but with the method we can clearly see the logic of solving it and it more intuitive. If we use formula that we memorize, we only can solve it but never had the deep understanding of why that formula works in the firsr place, and that is just like a robot,like here are the number now crunch that into this formula. I prefer the concept so that when we found a harder or unique problem, we still can solve it and not run out of ideas because we dont have a formula for it

@Zalamandar 3 года назад

Well of course it is. All methods must eventually lead to the correct answer, but some methods/formulae might just be easier/quicker/more intuitive to use for different people.

@shiiqu8174 3 года назад

@@ravindrawiguna8681 Most students won't need to have a deep understanding and they don't want it either.

@Etc2496 3 года назад

@@ravindrawiguna8681 I mean that's why you learn where the quadratic formula comes from how it's derived. But after you see that there's no need to pretty much derive it every time you want to use it. Just apply it directly.

@SK13736 4 года назад

In the end, we end up with the same process but in a different route.. but it does look more lengthy than the usual way tho..

@MathswithMuneer 4 года назад

Very true.

@zecuse 4 года назад

My list of steps for both methods, separated into trivial parts: Formula Video 1. b^2 Divide a 2. 2a -B/2 3. Twice the result * c Square the result then - C 4. Square root the difference with step 1 Square root the result (roots are obtained here for both) 5. Simplify the fractions if applicable Notes: Steps 2 and 3 of the formula can be very quick but are necessary for each result. Whenever I've had to deal with the formula in (grade) school, I was always told to simplify the result as much as possible to receive full credit, otherwise why do any of the work to begin with. My college math courses didn't care about simplifying unless it was explicitly stated. Dividing the a can be done across steps 2 and 3 of the video method. When your work needs to be shown, there's fewer places for error because you've already performed the simplification along the way to the answer. You'll notice the steps are the same for both methods, but the division is done first instead of last.

@NirateGoel 4 года назад

Expect for the -b you were unfair with steps 2&3 4ac is one step not 2.

@zecuse 4 года назад

@@NirateGoel 4ac is the same as doing 2a then that result * 2c. Again, I broke things down into trivial parts that mattered, hence why the subtractions are combined with the roots step. Calculating 2a is a necessary step in calculating 4ac, whose value is also required elsewhere in the formula. I even stated in the notes that this would be a reasonably quick computation compared to all the other steps.

@lunaticluna9071 4 года назад

"Mathematician finds a new and easier way to calculate quadratic equations" Yeah no it definitely wasnt him that found it

@Ignasimp 4 года назад

And it's definitely not easier lol.

@deivisony 4 года назад

@@Ignasimp y tho

@genieinthepot2455 4 года назад

....It was tho

@brightblackhole2442 2 года назад

@@genieinthepot2455 however important they were, they did not invent factoring

@FROFilmsIRE 4 года назад

When you say "everyone" is talking about this new formula, presumably you mean the tiny minority of us who go to RU-vid to muse about maths.

@scottcarothers837 3 года назад

Y’all like “only Americans didn’t know this” but i got taught this before the quadratic formula

@gunjannagda9526 3 года назад

True

@urisap9884 3 года назад

Same lol

@sjorsbarten8900 3 года назад

Me2

@buggyfifa 3 года назад

Same lol A and B were alpha and beta.

@siddharthdoshi4858 3 года назад

Lol same they taught us this method in 8th grade and quadratic one in 9th grade ig

@SeeTv. 4 года назад

3:45 Nice! You just derived the pq formula!

@lunaticluna9071 4 года назад

This is the pq formula.

@V-for-Vendetta01 4 года назад

Bruh

@maon7565 4 года назад

A: The quadratic formula is not difficult. B: This method isnt easier.

@valeryrus 4 года назад

It is easier if u get good numbers

@anmolsekhon3545 4 года назад

its been there for years its easier and in india its more famous

@VivekKumar-td3me 4 года назад

@@anmolsekhon3545 which one is easy for quadratic formula is easy

@KerrankiSuomee 4 года назад

This one has less to remember and it's easier to use without writing anything down

@puppetsock 4 года назад

It is harder. It’s the old method with the added thing of dividing by a.

@eliahabib9267 4 года назад

The "New Way" in this video is what they teach us in school in 9th grade.

@ryanmajumder9569 3 года назад

Ha ha ha sooooo true..👍

@kepler4192 3 года назад

Exactly

@ex_why_zee9126 3 года назад

It was taught in 7th to us

@siddharthdoshi4858 3 года назад

Yeah I remember I used to do it this way in 8th standard. My tuition teacher had taught me this and I clearly remember it was 8th grade coz that was the first time I joined a tuition. Those days were great!

@alifyasadikot6797 3 года назад

@@siddharthdoshi4858 agree🙋🏻‍♀️

@tomsharpe2185 4 года назад

This is just 'completing the square'. Completing the square for a general quadratic equation is precisely how you derive the quadratic equation. Soooo... nothing new here.

@Abhinav-ss3th 4 года назад

Check again. It is the individual steps that is used in the process. 'Z' is a new variable in itself. completing square uses number functions and the discriminant method to get the roots

@darthmath1071 4 года назад

@@Abhinav-ss3th no...unless we have a different definition of "completing the square"

@stelladavis1798 4 года назад

Tom Sharpe it's a little different than completing the square

@_-_-Sipita-_-_ 4 года назад

The original is like finding a product and a sum And the new one is finding a power 2

@telaferrum 4 года назад

They both work, but this is definitely not completing the square. 2 ways to get the same answer, but I like this one more since it builds on what we know about factoring. To complete the square you try to get a polynomial from standard form to (x + n)^2 + k Point being that (x + n)^2 is a completed square, so you can move k to the other side and take the square root. With this method instead you want a polynomial to go from standard form to something like a factored polynomial. (x - r1)(x - r2) Multiplying that out to standard form gives Vieta's formula which gives a straightforward 2 equations and 2 variables -B = r1 + r2 C = r1 r2 That's made simpler by showing the roots are in the form r1 = -B/2 + z r2 = -B/2 - z So then it's just 1 variable and 1 equation.

@detectivl5811 4 года назад

This method really only is new for Americans 😂

@detectivl5811 4 года назад

@@C4pt41nN3m0 Yeah cause this method is way easier to remember and can be used in more situations 👌

@frankjohnson123 4 года назад

It’s not taught because it’s just the same method with more room for error

@angelmendez-rivera351 4 года назад

frankjohnson123 That makes absolute no sense. If two methods are identical, then they have the same room for error. That is implied by the definition of identical.

@Last_Resort991 4 года назад

Videos like these really imply that americans aren't very intelligent 🤔

@GD-ep5fl 4 года назад

@@C4pt41nN3m0 esatto, si fa quando B è pari

@bobengelhardt856 4 года назад

"You don't have to memorize anything" Except a multi-step process with much more opportunity to forget some little, but vital, step. Way, way harder than just memorizing Brahmagupta's formula!!

@theterribleanimator1793 4 года назад

At this point you might aswell make an algorithm for finding the root for any type of function.

@nojomyth 4 года назад

I find it way easier to remember as - p/2 +- sqrt( (p/2)^2 - q) xD It's also way faster to tell if there's a solution in R for the equation without the need of a calculator since u can just approximate it x^2 + px + q

@piman9280 4 года назад

I was always told it was called *The* Quadratic Formula.

@user-mc8wg6qq3b 3 года назад

@@piman9280 Hmm, it was discovered by that man, so its sometimes also called brahmagupta's formula

@aaash2952 4 года назад

Americans- Whoa that’s a new way to solve Quadratic Equations ! Meanwhile in India- Grade 8 students solve via this method.

@cullinan1611 4 года назад

Bhai konse school m ho ?

@night23412 4 года назад

grade 10*

@kavithajagdeesha8999 4 года назад

@@night23412 grade 8

@yldrm5704 4 года назад

@@kavithajagdeesha8999 10 for cbse

@ishanjain922 4 года назад

Bruh I'm in 8th and I do the middle term split

@zwest808 4 года назад

"an easier way to find the roots." :/

@mwexim7132 4 года назад

Zack West I agree. The ‘common’ teached way is easier to memorise. This formula is indeed easier for beginners, but you’ll need to meorise more steps, and that’s not what mathematicians want to do.

@zwest808 4 года назад

Mwexim yeah. There are already so many easy methods to find x for quadratics. If they’re going to find an easier way of memorizing types of functions they should do it for higher degree polynomials

@Ibakecookiess 4 года назад

@@mwexim7132 This way at least you understand what's going on. Memorizing a formula isn't learning much...

@lukamitrovic7873 4 года назад

@@Ibakecookiess you don't really understand much lol. It's literally the way you derive the formula, nothing else

@mwexim7132 4 года назад

@@zwest808 The problem is, it is proven that for 5th degree polynomials, you can't find a method for discriminants, so that's indeed interesting.

@johndoeanon445 4 года назад

When I saw this, I thought for a moment: "I wonder if it's just going to be a complicated way to do the PQ-formula". A few minutes later, lo and behold.

@nowonmetube 4 года назад

To me actually the beginning formula looks exactly like the pq-Formel, say what? O_o

@RegorForgot 3 года назад

God damn you and your pun

@OriginalSuschi 3 года назад

nowonmetube ah I love the PQ-FORMEL (speak it out loud in a very german accent). Ich mag die Mitternachtsformel mehr als die PQ-Formel (auch wenn's irgendwie das gleiche ist...)

@pruthvishthakkar151 4 года назад

Mathematicians: This is new way of solving quadratic equations Indian teachers (teaching this to students for decades): Hold my chalk

@ashishmeshram5057 3 года назад

Indian teachers op 😂😂

@redskull4447 2 года назад

Yah -b+_(b²-4ac)^½ -------------------------- 2a

@bishiyarudesu 2 года назад

@@roastedpeanuts694 this is a certified good classic

@krishanuchattopadhyay7006 Год назад

@@wockhardt69 And still 45% of your NASA employees are Indian, PM of UK is Indian. 😂😂😎😎

@krishanuchattopadhyay7006 Год назад

@@wockhardt69 When you google remember Sundar Pichai an Indian is the CEO of it. Whenever you count money remember 0 is given by Aryabhatta an Indian. Trigonometry was given by Indians, Baudhayan theorem was taken by Pythagoras and took the patent. So, stop lecturing us, India is the best. AUM 🙏🏻 MAY BUDDHA, NARAYANA, SHIVA give you some buddhi (intellect) to think 😁

@yashrawat9409 4 года назад

In India you never learn the quadratic formula till 10th class (high school) Before that the children are taught the product and sum method, but not motivated to generalise it

@phamnguyenductin 4 года назад

Here in Vietnam, students learn the quadratic formula in the 2nd semester of 9th grade. It's pretty close.

@devansh3700 4 года назад

Yeah and this method is called splitting the middle term

@tumhregfkahusband8725 4 года назад

I am from india and i learnt quadratic formula in 9th grade

@humaneBicycle 4 года назад

@@tumhregfkahusband8725 he is talking about cbse and not icse or state board

@dinul1719 4 года назад

Same here in Sri Lanka

@timoriusmaximus 4 года назад

Here in Germany this method is very well known as the "pq-Formel" ("pq-Formula") and definitely nothing new.

@theraytech54 4 года назад

It's only similar and he talks about it

@koldovalnya 4 года назад

Or "Vieta's theorem"

@kallewirsch2263 4 года назад

@@theraytech54 It is not similar. It is exactly the same. Just all the individual steps combined into 1 formula. The derivation of the pq formula however is usually thought in a more geometrical way. But if you think of it, what is done here is not that different from "completing the square" in an algebraic way. I am not to say, that this derivation is bad or anything like that. It is a nice derviation. But to call it "new" is way beyond what it should be called.

@takvacs 4 года назад

I'm sorry to be butthurt over here but this is just like that time I thought I had figured out a general equation to calculate the sum of natural numbers only to realize some Gauss dude did that a few centuries back. All the more power to anyone helping people that don't yet know this. Lord knows math needs to be made fun for all.

@cizma27 4 года назад

When I was 12 we started doing geometry and learned pythagoras. I realized about connection between angles and opposite sides. I had full notebook of my findings, mostly ratios between longer and shorter side of right triangle. I also had some breakthroughs when I started drawing circles around right angle triangles. My teacher told me that I was on a good path and too keep working. It lasted for a month or so. 2 years later I started the high school, we started doing trig and it all flashed back to me. Basically I (kind of) reinvented tan function as a 12 year old.

@aarushrathore1276 4 года назад

As a child what i did Sum of infinite nos is -1/12 and also general formula is n(n+1)/2 and equal them.

@darkseid856 4 года назад

@@aarushrathore1276 lim(n -> infinity) {n(n+1)/2} = -1/12

@Preeesco 4 года назад

I remember that some years ago I had discovered that a²=(a-1)²+a+a-1 Eg 6²=5²+6+5. Then I realized it was just an "application" of (a+b)²

@mdzaidhassan8996 4 года назад

Me too as 7 years old figured out to calculate sum of continuous natural numbers by adding first and last term and for others..

@AShu-ey9zu 4 года назад

Thanks sir. Your videos are great inspiration for me and my students to explore new horizons of maths as I have been also involved for preparing students for class8 maths Olympiad at my school level and we have won last year gold for our campus amongst 18 campuses participants.

@TheScienceGuy10 3 года назад

3:56 Substitute the value of B and C as -b/a and c/a and voila, you have the quadratic formula :)

@shade5554 3 года назад

Bruh, I was so utterly disappointed watching this video, thought he was gonna talk about some revolutionary way of finding roots

@anurag95sharma 4 года назад

The quadratic formula is easier to memorize. This method(in the video) is intuitive(easier for beginners) but still requires memorization of steps. The beauty of quadratic equation formula is the √(b^2 -4ac) part of it: This part tells you whether the roots are real, imaginary root or single root.(Discriminant) This formula also gives us the shape of the parabola that the equation forms. For beginners memorising the formula is difficult but as you dive deeper into mathematics, this formula looks elegant.

@extremeextraordinary5588 4 года назад

Nerd

@Lolwutdesu9000 4 года назад

Err, every parabola has the same shape. The only difference is that they are scaled with different constants.

@ashishkale5424 4 года назад

b^2-4ac is called as discriminant not determinant!!

@kariminalo979 4 года назад

It's called the PQ-formula and it's way easier to remember than the Quadratic formula. You re-arrange the second degree polynomial into the form of: x^2+px+q hence to get the roots, simply plug in the coefficient "p" into the main pq-formula which follows below: x=-p/2±√((p/2)^2-q) If p < 0 then you'll have p/2 before the square root, it doesn't matter what what the whether p is negative or positive in the square root since it will always become a positive number after being squared in side the square root. If q < 0 then it will be written as +q in the square root and if q > 0 then it will be written as -q. For more detailed overview just check out the link of an image that I have attached below: images.app.goo.gl/fEm2U8BJXsa48Z7j9

@anurag95sharma 4 года назад

@Adam Romanov My point was it shows where the graph cuts on the x-axis. I thought it was implied in my answer. My bad.

@carrotfacts 4 года назад

You’re memorizing a whole method that explains exactly what the quadratic equation is DOING. In fact it sounds even harder to memorize as it’s wordier. It’s much easier to know the quadratic equation

@UltimateBargains 4 года назад

3:46 I recognized the classic quadratic formula when he got to ±√ thing.

@ruthsquire958 4 года назад

No, it's not. It's easier to know a formula but it's better to learn a method. Always. That's because embedded within the method is the formula.

@SlingerDomb 4 года назад

Should be great to teach kids about this instead since mathematics is all about following logic and thinking not purely memorizing.

@chrisbhaus5813 4 года назад

I am from Germany. I'm 36 years of age and even my mom learned this "new" method at school. In Germany every student older than 16 knows this method as the "PQ Formula". And this is since...I don't know...Kaiser Wilhelm, I think 😂😘

@Negs42 3 года назад

Haha same..I'm from Germany too..

@thetntsheep4075 4 года назад

I find it easier to complete the square. Maybe just because I'm used to it 😁

@AniketKumar-cs9wb 4 года назад

I already have seen this 5 min ago

@MindYourDecisions 4 года назад

In that video at 1:10, Achrotone noticed the typo "back-to-bank" which is now corrected: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lDbQA4euAbY.html&lc=UgwYAupZwmfkh8Nfred4AaABAg

@fix5072 4 года назад

@Shailesh Kumar true, and the formal description is easy for everyone to do it theirselves. I'm from Germany and we learn this formula from 5th grade (10yo) and I never knew this wasn't taught in the entire world 🤷‍♂️

@AshutoshIIT 4 года назад

@@fix5072 yes...& That formula is invented in India....& now used in all over the world 😃

@adi-sngh 4 года назад

@@AshutoshIIT ok boomer

@annapurnarangrej4221 4 года назад

@Shailesh Kumar hey Bro, already our quadratic formula was derived by dividing 'a'😄

@kobe11111 4 года назад

I have a question. Where exactly is this regarded as a new method? Because I learnt this exact technique 5 years in high school...

@MrHatoi 4 года назад

Where did you go to high school? I'm pretty sure they don't teach it in most parts of the US but they do teach it in some countries.

@kobe11111 4 года назад

@@MrHatoi I actually went to high school in Jamaica and that's how they teach it across the island.

@MrHatoi 4 года назад

@@kobe11111 That's interesting to know. I went to school in the US and I never learned this.

@kobe11111 4 года назад

@@MrHatoi live and you learn I guess 🤷🏾‍♂️

@eRayPeitz 4 года назад

I'am from Germany and we get taught the first part of this method under the name "PQ"-Formla. x = - (p/2) +- sqrt( (p/2)^2 - q ) I always were mad that we not got taught about the abc-formula because for some equations the division with the a factor wasn't that easy. This method really helps me, because I like the quadratic approach is rasiert than the root approach.

@mousumibhamjasanyal5506 4 года назад

It's the commonest method of solving a quadratic equation in India.

@molamola8305 4 года назад

This is not any "new" way.It just resulted from the property of quadratic coefficients.Everyone who knows Brahmgupta's formula knows this.

@skwbusaidi 4 года назад

Inteseting mthod . But if the forget the quadratic formula, I will do completing the square which is not harder than this method x^2-8x+15=0 x^2-8x=-15 x^2-8x+16=-15+16 (x-4)^2=1 x-4 = 1 or x-4 = -1 x=5 or x=3

@avrilcadeul3207 4 года назад

This is the method that should be in the video ! 😂

@ugurcansayan 4 года назад

"Complete squares" is like the ancient proof for life, time and everything! :)

@karinano1stan 4 года назад

yeah, our algebra professor showed us that way

@Raghad-hc7nn 4 года назад

Sami can someone explain where the 16 came from?

@Raghad-hc7nn 4 года назад

Sami is it a method to make -15 become 1 or 8x2

@feelthereal5742 4 года назад

Can you make a video on solving cubic equation without guessing any solution. I want you to do that because your explanation is good.

@vasileiospapazoglou2362 4 года назад

You don't guess in cubic there are formulas and other methods to solve them.

@detectivl5811 4 года назад

x^2+bx+c = 0 x^2+bx+(b/2)^2-(b/2)^2+c = 0 (x+b/2)^2+c-(b/2)^2 =0 That's even easier than remembering the formula, cause this is just common sense

@siveroo7493 4 года назад

@@vasileiospapazoglou2362 yeah but that's so complicated, and guessing the roots seems like a better method to go, although not really effective

@user-xb9yv2ci4c 4 года назад

There is the cardanic formula for this.

@feelthereal5742 4 года назад

@@user-xb9yv2ci4c suppose I forgot the formula. Now there should be a straight forward method to find the solution.

@nesha_owo 4 года назад

when it's Christmas break, but Math is still haunting me from my recommendations :3

@madhuawasthi993 4 года назад

First of all it's not bhram Gupta's quadratic formula it's Shridharacharya's quadratic formula

@Sailed_away 4 года назад

Both were from India , so kindly shut up ....

@pragul1999 4 года назад

@@Sailed_away well its like saying George Washington and Donald Trump are both america's presidents hence they are the same guys

@bidishadey3815 4 года назад

Exactly, this is sridhar acharya

@akhil3271 4 года назад

@@pragul1999 ,😂😂😂😂😂 You made my day

@piman9280 4 года назад

Better still, *THE* quadratic formula.

@Kanoemirate 4 года назад

This approach looks more time demanding and it's not a new thing. I learnt in back in Secondary school in late 90s. And in Nigeria🇳🇬

@tamirerez2547 4 года назад

I gave a LIKE just because the last line: and in Nigeria...

@StRanGerManY 4 года назад

@@tamirerez2547 mentioning Nigeria makes any comment funny!

@paweplewa3644 4 года назад

When you had known this method before you watched the video *A Genius* But then you looked at the comments.

@humanityisnumberone6008 4 года назад

Nope,this is just a simple mathematics at 9th grade

@paweplewa3644 4 года назад

@@humanityisnumberone6008 Not in my country ;), It's just a joke man.

@Icy-ll5ie 4 года назад

@@humanityisnumberone6008 my teachers have not thought me this method

@pallabgoswami2451 4 года назад

Absolutely it I knew this when I was 13

@paweplewa3644 4 года назад

@@pallabgoswami2451 Same as I. But in Poland we aren't taught this method, It is not in our schools.

@randomguy8461 4 года назад

This is just quadratic formula with extra variables and steps, @4:09 it's literally exactly the same thing only it has been chosen to write C in place of c/a and B instead of b/a. I feel like I would be less upset if this wasn't called "a new method" (i.e a way to completely avoid the quadratic formula) but instead called something like "a new way to derive the quadratic formula" or something similar.

@anthonypazo1872 2 года назад

I had never been taught this before, but now that I have seen it, it seems so obvious. Well done explanation of this process.

@aniketroy805 4 года назад

Here is nothing new.....you have just solve it by using shreedharacharya's formula.....just a another proof of the shreedharacharya's formula

@gaurangrajai401 4 года назад

Could you plz share any information about it( Shreedharacharya's formula), I'd be grateful to you.

@Salien1999 4 года назад

Any method that solves a quadratic equation can be used to prove Sridhacharya's formula, since the resulting solutions will be equivalent. The way we should judge methods like these is by how easy they are to remember and execute. This method, while more intuitive and easier to remember than Sridhacharya's formula, takes a few more steps to do. Therefore, neither is inherently better. They are both useful, for different circumstances and mathematicians.

@aspiringscientist1616 4 года назад

Are u from Agartala?

@realhawaii5o 4 года назад

I feel like the Quadratic formula is much more useful. Having studied maths until the end of high school, and now having calculus and algebra in university, I feel like having the discriminant is quite useful. As you delve deeper into maths, the formula is more useful than this alternative method which might seem more intuitive for beginners.

@calebking1608 4 года назад

You don’t have to throw the discriminant out the window though. This method is simpler.

@anitagofradump5195 4 года назад

I wish i knew this method for some of my pure maths classes in diff eqs when the type of roots didnt really matter than much and we were forced to solve them no matter what. (And we werent allowed calculators so i think this method woulda been easier to do by hand than the quadratic eqn)

@Michael-zn2jc 4 года назад

R2D2 from Star Trek I prefer the quadratic formula. It’s a formula and it’s good to solve any quadratic equation. I’ve used it so many times it’s almost impossible for me to forget.

@smcmaison7845 4 года назад

This is basically "Completing the Square" in a nutshell. 😄

@piman9280 4 года назад

..... or not using a sledgehammer to crack a nut.

@mvpistakenbyme818 3 года назад

Bruh no both are entirely different things 😂😂

@smcmaison7845 3 года назад

@@mvpistakenbyme818 its the same tho. Try using CTS in the problem and you'll see the difference. Even QF is CTS with a memorizable formula. There is generally only 2 ways to solve Quadratic Equations. The factoring method and Completing the Square Method 😂🤣

@nicholasaldrich8419 4 года назад

Isn’t this literally explaining how completing the square works lol?

@yurenchu 4 года назад

No, because completing the square doesn't utilize the concept of finding two numbers that are symmetrically positioned on each side of a given "average" m . Completing the square: re-writes the quadratic equation into the form (x+p)² - q = 0 This method: re-writes the quadratic equation into the form (x-u)(x-v) = 0 where u = m+d and v = m-d , for some fixed values of m and d. However, they are related by the insight that (x-p)² - q = 0 can be directly re-written as (x+p-√q)(x+p+√q) = 0 which means p coincides with -m , and q coincides with d² . (And of course they must be somehow related, because they are solving the same type of equation.)

@karthie003 4 года назад

Yeah its basically completing square method. Also love the profile picture btw!😂 I love Brendon urie😂

@michka841 4 года назад

Mathematicians : how to solve equations Engeneers : *DØ ÅPRŌXĮMĀTÎØNS*

@OlavurNonE 4 года назад

“But the key insight in this method is that you dont have to memorize anything” Yeah sure...

@justinsir 3 года назад

You people are using calculator So, No need to memorize tables No need to memorize square root. No need to memorize algebraic identity (a-b) (a+b)

@AndriiBilous 4 года назад

Dear author! Where were you with your video 30 years ago when I was at school! That's great method, damn!

@tonksonk951 4 года назад

I saw this article a few weeks ago, nice to see a video on this :) Though, my biggest qualm with this method is the fact that if the coefficient A is not equal to 1 you have to factor the function into that form which can result in B and C becoming cumbersome fractions. Other than that it's a really nice way to be able to think about the roots and the mathematical intuition behind them.

@probropalzlive6961 2 года назад

Or, as Indians are taught, for the quadratic equation ax²+bx+c, find p,q such that p+q=b and pq=ac. Thus, -p and -q are the roots of the equation.

@aguyontheinternet8436 2 года назад

fractions aren't that hard to deal with. Math can throw a lot worse at you than a couple ratios

@dinnerxet 4 года назад

Me: does this method Teacher:Well yes but actually no.

@michaelz2270 4 года назад

People should stop calling this a new method. Anyone who has graphed a parabola can see that the roots are going to be of the form m +- n where m is the x-coordinate of the vertex of the parabola, given by m = - B/2 in your notation. Yes, in the centuries people have been solving quadratic equations, people have tried plugging in - B/2 +- n and solving for n. If they know a little more they'd set the product (-B/2 + n)(-B/2 -n) = C and solve for n. Seriously, this needs to stop being treated as something new. All these fancy degrees being shown off just make the situation more infuriating.

@Anathorn7 Год назад

You do a very nice job teaching in such an interesting and eye-pleasing way! :) Could you please tell me what program do use for this kind of animations?

@KumaKaori 4 года назад

Cripes, any article I read on this mess was incomprehensible. This video makes it make /a lot/ more sense. Thanks Presh!. I genuinely don't know how much of this process and or the cheat steps I may have been taught in school. Been too long and I figured out how to get my ti-89 to solve the tricker ones for me quite early.

@TheXzasxz 4 года назад

I still find the method I've been tought over 30 years ago the easiest to remember and provide. What you need is to always remember two equations: (x+a)^2= x^2+2ax+a^2 and (x+a)*(x-a)=x^2-a^2. Simple example is x^2+6x+8=0 x^2+6x+9-1=0 (x+3)^2-1=0 (x+3-1)(x+3+1)=0 (x+2)(x+4)=0 So we have the solution.You may notice, that if you try to solve a general equation ax^2+bx+c=0 using this method, you will get the quadtratic formula, which was always hard to remember to me...

@deadfr0g 4 года назад

Video length: Eight minutes, eleven seconds My reaction: QUICK MAFFS

@aaronwarwick9966 4 года назад

I came up with this method when I was about 12. But not for doing quadratics, I had no idea what they were. I was using it for a "magic" trick that I made up, and this was a quick way to get people's answer. When we learned the quadratic formula I told my math teacher I'd come up with something similar, and I thought it was a tiny bit easier. He said "nah. Shut up and write down the equation". Love of math ended that day...

@taskmaster4624 6 месяцев назад

oh boy i feel bad for ya

@San-lh8us 3 года назад

"a key insight in this method is that you don't have to memorize anything" proceeds to show what you need to memorize to use this method

@thecaretaker0007 4 года назад

I derived the quadratic formula myself when I wasn't able to memorize the formula ... And then I didn't needed the formula to get roots.

@scottierna5831 4 года назад

It is not just similar to what's taught in Germany. It is exactly what I was taught in my German high school. But our teachers explain it easier😂 You can use the stuff in the square root for finding out if the function is a passant, tangent, or secant line as well. In the complex method the factor a is just integrated, but that confuses students and/or lead to small mistakes you do even if you know how it's done.

@mango5030 3 года назад

Literally what we study at class 10

@francogonz 4 года назад

But the "formula" at 3:58 isnt exactly the same than original quadratic formula by reemplace B and C?

@martinthemaverick6052 3 года назад

You need some math class xD

@policarpo4816 4 года назад

In Italy we are taught a similar thing as a shorter formula for quadratic equations when b is even. If a=1 (which is in this case done by dividing everything by a) you get exactly that formula. Also, the new formula is not so easier to remember than the normal one

@zemp9671 4 года назад

I’m italian too, and i can tell that this is off topic. I mean, it is true that you can simplify the quadratic equation but this has nothing to do with the method explained in the video

@policarpo4816 4 года назад

YOLO Zemp the topic is indeed different and we use different demonstrations, but the formula is still the same

@lorenzot.7045 4 года назад

In poche parole hanno scoperto l'acqua calda

@policarpo4816 4 года назад

lorenzo timpone esattamente 😂

@gabrielenicosia7121 4 года назад

Si, la formula del “B Mezzi” con il B pari

@viewer4229 4 года назад

Sridhracharaya formula 🙏🙏🙏🙏🙏

@antipro4483 4 года назад

I just tried to say that name and now the world is upside down

@viewer4229 4 года назад

@@antipro4483 it is simple, but not easy!!!

@prashantdahiya711 4 года назад

You have changed my life by telling is method.

@haljordan4082 4 года назад

I'm gonna solve quads my way.

@erikkozhevnikov3444 4 года назад

actually, when you're dealing with parameters and very small numbers which you mostly will it just becomes more complicated, thats why you teach the formula, this method is only good for convenient numbers in easy problems.

@ajfalo-fi3721 4 года назад

Exactly, the examples given here were pretty convenient numbers

@anuragsuresh5867 4 года назад

In the UK everyone that does Further Maths learn this in a topic called roots of polynomials.

@MathswithMuneer 4 года назад

Very true, Hi, I am making Videos for O\A levels as well. Please feel free to check them and do share your feedback.

@rody3199 4 года назад

What about equations with bigger exponents? Could there be an intuitive method like this one out there for those?

@harshraj447 4 года назад

In India, even 8th class students know about this method as factorization method. We have even made various tricks to make this way ever faster. Hence, nothing new for me. 😂

@peterprastakos9152 4 года назад

lol right, let me know when India starts beating the US in the math olympiad

@random_shit_online6104 4 года назад

@@peterprastakos9152 🤣🤣

@Singh-be2qn 4 года назад

@@peterprastakos9152 good morning

@aamitanandd 4 года назад

@@peterprastakos9152 lol let me know when American firms stop hiring Indian CEO.

@MyReligionIs2DoGood 3 года назад

@@aamitanandd Nice burn! :)

@PartyMain 4 года назад

This method also allows you to find the middle (aka top value) of the function. I knew there was possibility to find x-values through addition/subtraction of the x value of the top

@aryanmadhwani 4 года назад

I'm solving from this method since childhood 😂

@ypn.official 4 года назад

We Indians are a step ahead than the whole world but we a too ignorant of ourselves... *Edit:* I was just trying to be a tad bit patriotic & was pointing out how we ignore our own potential... If the comment appears kinda racist 😑

@keyboardcorrector2340 4 года назад

*Galaxy braining intensifies*

@VivekSingh-ts1ec 4 года назад

@@ypn.official don't say like that. It seems to be a racist comment.

@Toryo. 4 года назад

In italy too...

@detectivl5811 4 года назад

@@ypn.official Its not only Indian... It's everywhere but the USA 😂 (In Germany we know this method too in 7th grade or so)

@amingholizad 4 года назад

this is exactly the quadratic equation and how it came to be. when first taught the teacher shows how we came about this formula so we can use it confidently knowing why it works

@atharvachaudhari6325 4 года назад

In this lockdown period this video was one of the best that i have seen for revision 😃😄video was awesome 😃😄

@priyankandatta5644 4 года назад

Like in icse, we know this in class 7. Thats like when we were 12 year olds.

@keyboardcorrector2340 4 года назад

I was reading Wittgenstein and solving advanced integral calculus problems at age four my guy.

@megacahh870 4 года назад

@@keyboardcorrector2340 lmao

@nabeelkhan4910 4 года назад

Ikr

@stigastondogg730 4 года назад

That was my thought - it’s the method of “completing the square” which then works out to be the quadratic formula anyway. In exams when asked to derive the quadratic equation, this is the method I used

@helobhay9427 4 года назад

@@keyboardcorrector2340 This is nothing.. We start perp for IIT JEE from junior kg and till 4th we're on top of the world.... Sarvashaktishaali Gaitonde🤣

@dhruvbhargav1547 4 года назад

@VishalMaurya 4 года назад

I know it, cz im in 10th

@saikalyan5559 4 года назад

Even 7th class student know this

@aashayagrawal1334 4 года назад

I am doing engineering and i didn't know it 🤣🤣

@aashayagrawal1334 4 года назад

@@dhruvbhargav1547 shame on me 🤣

@aashayagrawal1334 4 года назад

@@dhruvbhargav1547 This formula is pretty good but doesn't gives us the discriminant which is important. You arts with maths 😧 you are pretty brave

@shivamsoni9820 4 года назад

In India we learn it in 7th standard while real formula at 9th

@manojmohan9893 3 года назад

And here I was worried that I missed some easy method of solving quadratic equations in school. I studied in a CBSE school(that's the central education board in india) which is average in terms of difficulty across our country. Some of the states do have tougher syllabus. And I still remember learning this method, which in india we call substitution method for deriving solutions to a quadratic equation( I may be wrong in naming). What I do understand from this video is that there does exist a difference to approach to math education in india to US. In india, we may have relaxed approach towards every other subject. But when it comes to maths we are actually very rigorous towards learning by practice rather than remembering a simple formula. Infact we are usually taught the long method of calculating something before we even learn to use a formula.

@rankanidhibehera5527 4 года назад

This is brahmagupta formula this is sridharacharya formula

@ViratKohli-jj3wj 4 года назад

@Victor Yago you too brutus

@edwinchang2760 4 года назад

I've seen this method a lot

@MathswithMuneer 4 года назад

Thats cool, and how about videos that I have for several topics ?

@arianagandhi7595 3 года назад

I've never in my life have used the discreminent method. I have this method in my years old textbooks.

@srishtisingh3986 3 года назад

In India we are taught the quadratic formula in 10th & 9th and the ways in these videos which are middle term split and related things in class 8th or below

@whyareureadingthis6719 4 года назад

To be honest I can't see how this makes it easier, u just took the quadratic formula and simplified it

@user-xb9yv2ci4c 4 года назад

In Germany, we learned in school first something we called "quadratische Ergänzung", which could be translated to quadratic completion. So, one adds and subtracts a number, so that the formula becomes (x-d)^2+e=0. In the next lesson, we derived the quadratic formula out of this.

@user-xb9yv2ci4c 4 года назад

Fun Fact: We call the quadratic formula "midnight formula" because it is so important, that you must be able to recall it, even when you are woken up at midnight.

@whyareureadingthis6719 4 года назад

@wise ol' man yeah that's what I meant to say, but I can't see how it's easier than just knowing the quadratic formula, it feels like u added some extra steps to it

@whyareureadingthis6719 4 года назад

@@user-xb9yv2ci4c we never learned something like that here, we just learned the quadratic formula straight away

@gilbertlondre2497 4 года назад

0000000 0000000 in the USA (and maybe other english speaking countries we call it “completing the square”

@Kairikey 4 года назад

But wait......... Looking the -B/2 +/-z, wouldn't it actually also be that z= sqrt(B^2 -4C)/2? Considering that the a of the quadratic formula in this situation is always =1 then this is still the quadratic equation.(I mean, duh) If B^2/4 - z^2 = C, then z^2 = B^2/4 -C or (B^2-4C)/4. Then z = +/-sqrt(B^2-4C)/2. That's an interesting way to think about it. So in the end, this method is simply a quadratic formula through a new perspective that are more intuitive, or simply also a way to make sense of what the quadratic formula actually represents. In other words, quadratic formula can be thought of as the average of B +/- an identity that is related to B and can give a product of C.

@detectivl5811 4 года назад

Yeah this is pretty similar to the quadratic formula 😅

@vaibhavm8043 4 года назад

Absolutely amazing. It's really very easy and will be helpfully throughout. Thanks alot.?

@jeffplease 3 года назад

damn when i used this in school and i was only one to do that on classes as a student, my classmates were staring at me like im cheating haha

@billord 4 года назад

This is a massively convoluted method. No wonder I've never heard of it

@abhinavmanawat4916 4 года назад

At 9th grade we were taught three methods to solve quadratic equations. Out of three ,two are described in the video. If you know the third one then like the comment😁😁😁😁😁😎😎 Hint: alpha squared /b1c2-c1b2

@HimanshuSharma-mv4sg 4 года назад

Factorization method (Splitting middle term), Completing square method, and Quadratic formula

@Jnoel608 4 года назад

As an American, I feel like we learn the most complicated unintuitive ways to do everything. Just to be different. (Edit) never mind. It’s really the same as the quadratic formula, just slightly different way of thinking about it. Depends on what you prefer. Remembering the formula vs remembering the concepts.

@aymanenouhail5241 3 года назад

the quadratic formula is easier xD it's plug and play, you can't go wrong with it. This one has a higher degree of error and requires more steps. I'll pass. you also get shown the proof for the quadratic formula when you get taught for it (at least here we do) so if you don't intuitively understand it it's your fault for not paying attention in class. Not that you really need to know the proof since the formula is elegant and short.

@EinApoStein 4 года назад

I realized the "pq Formel" immediately. greetings from Germany

@e1coachingcenter 4 года назад

Nothing new, already using it for last 3 years

@Tusharsharma-lm8bd 3 года назад

So you took your content from such places and then teach that to your students on your name It's a shameful act

@goutammandal2968 3 года назад

Hii sir

@MsMumuku 4 года назад

From my experience as a math teacher, even though students know both methods, most will prefer Brahmaguptas Formula because they can just plug everything in and the solution falls out. They will even use it if the solution basically jumps at them. Mostly students for which math classes aren't a constant state of hardship will take a second to consider what might be a quicker or easier way. Cheers to all the people in the comments who are vocal about finding this trivial. Thanks for letting everyone know.

@Ni999 4 года назад

Well said.

@CharaNoTame 7 месяцев назад

This is also known as the PQ-Formula, we were told to memorize it (in my case). However I've also seen students remember this formula with some rules of thumb. (0. make sure the equation is x²+px+q=0, and not let's say 2x² or so) 1. divide the middle term (p) by -2 2. add the +- symbol and draw the square root, then square the term from step 1 and put it inside the square root 3. subtract q (also inside the square root) formula will look something like this x = (-p/2) +- sqrt((p/2)²-q)

@Vzduch2 4 года назад

I still think that solving them on a case by case basis is better, I never liked the quadratic formula and rarely ever use it, but I learned it anyways, because it's just simpler to use it when the numbers get too large or irrational.

@paoloposo 4 года назад

I've been to school in Germany and I can't recall ever having learned a method to solve a quadratic equation that involves guessing. I could never remember the ABC formula when I was in school so I used the completion method and it is still my preferred method today.

@kqvonpc3999 4 года назад

I knew that method before.Also we use it at school.

@MathswithMuneer 4 года назад

True, there is nothing new in it. You can see my way of teaching as well.

@Lucifri 3 года назад

In Brazil, we are taught to solve using the general formula, but it's called the Formula of Bhaskara. Bhaskara II was who complemented Brahmagupta's formula and ended up with the solution for the general case. en.m.wikipedia.org/wiki/Bh%C4%81skara_II