Examples: A Different Way to Solve Quadratic Equations

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If you'd like to continue learning in this style, Prof. Loh runs a systematic course series which focuses on teaching people how to invent their own mathematical techniques (live.poshenloh.com/), as well as regular streams on this RU-vid channel.
Want to understand how to solve any quadratic equation, without just memorizing the quadratic formula? In this lesson full of worked examples, Daily Challenge founder, Carnegie Mellon University professor, and U.S. International Math Olympiad coach Po-Shen Loh introduces a simple, different method for solving quadratic equations. Instead of guess-and-check, this method uses students’ existing experience searching for a pair of numbers with a given sum and product to solve quadratics.
This video explains all of the details behind Prof. Loh's initial quadratic method video (ru-vid.com/group/PLqv4sKOD1b..., including different examples of how to use the method to solve more and more general quadratic equations.
Prof. Loh came to discover this method because he has been systematically thinking about how to explain school math concepts in more thoughtful and interesting ways, while creating lessons for our Daily Challenge (live.poshenloh.com/).
Thanks to the Templeton World Charity Foundation for their support of this work.
==========
UNIQUE APPLICATIONS OF THE METHOD
Looking for a specific kind of problem that this method can solve? Check out the timestamps below:
21:24 Coefficients with different signs
25:03 If the coefficient of x is odd
27:28 If x² has a coefficient other than 1
30:41 Deriving a Quadratic Formula
33:14 Deriving the commonly learned Quadratic Formula
HISTORICAL PARTS OF THE SOLUTION
38:18 Viète’s Relations
39:00 Babylonian Mathematics
==========
ABOUT DAILY CHALLENGE
The Daily Challenge with Po-Shen Loh is a series of online math courses designed to teach people how to invent, taught by an actual inventor. The novel teaching style continually presents students with problems that they barely don't know how to solve, and guides them to invent their own solution methods through hints. It covers a wide range of ability levels, starting from basics which only require Pre-Algebra, and reaching up to university-level topics such as Number Theory. Instead of simply teaching the standard curriculum earlier, it goes deeper, providing additional challenges outside of the classroom. The course series also provides an efficient way to systematically cover math competition topics. To learn more about Daily Challenge with Po-Shen Loh, visit daily.poshenloh.com.
ABOUT EXPII
Expii is a free math and science education platform that embraces what makes us all individuals: our voices, experiences, and cultures. We encourage choice and experimentation by giving students the power to choose how they learn. Through creative, fun, practical, and personal lessons each person can have their own aha moment.
JOIN OUR MAILING LIST
If you have a middle schooler who is interested in thinking deeper about math, join our biweekly newsletter to learn more about math competition information, education news, and the inside scoop on all things Daily Challenge with Po-Shen Loh. Subscribe now by visiting www.eepurl.com/gExYzT.

Опубликовано:

10 дек 2019

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Комментарии : 1,5 тыс.

@BravoTango-vt8em 4 года назад

This is the type of math teacher I like. The teacher who actually lets their kids understand the math instead of making them pass the exam so he doesn’t have to worry about it again.

@muhammadazeem9775 4 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L4ImyFn1xLk.html

@ashishkushwaha2214 3 года назад

Right bro

@aravinds3846 3 года назад

I wish I saw this lecture before JEE exam lol. The graph method makes the questions INCREDIBLY easy

@ooffoo5130 3 года назад

he also has an iq of like 230 so that might have something to do with it

@antoniofuller2331 3 года назад

Hmm

@robertmcfarlane8546 4 года назад

This is one of the best lectures on quadratic equations I have seen. Thank you Mr Loh for clear and understandable information presented in a concise manner.

@psloh 4 года назад

Thanks for your feedback!

@Morningstarintheroses 4 года назад

@@psloh sir, could you please reply me??

@muhammadazeem9775 4 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L4ImyFn1xLk.html

@d.chandrasekara7959 2 года назад

Why 14 doesn't become -14 as in x^2-14x+24, can someone explain it pl

@jimspelman8538 3 года назад

I am a math and computer science major and a math teacher (middle school) and, like others have commented, I have never seen this method before. I love how you can easily get non-integer solution sets! Perhaps instead of the "Po-Shen Method" I shall henceforth call this the "Magic Quadratic Po-Shen" (just to add a little wordplay)!

@chocolateangel8743 3 года назад

I saw a video in which a college professor did the same thing -- because he couldn't remember how to pronounce his name.

@Tweeting_data Год назад

Portion

@rajeevmaakan1347 4 года назад

I salute you man! This is absolutely amazing....have been teaching math for 35 years, you have just made my job easier for whatever remaining number of years I will be able to teach. That's why they say....it doesn't matter you learned something new so late in life, what matters is you got new knowledge (new, I say, for the learner), new wisdom. And last but not the least, what is the primary objective of Problem solving....in any branch of knowledge or education....it is to achieve the objective in as simple and as uncomplicated a manner as possible....so that it can bring a smile on the faces of our students. Thanks a zillion bro!!!

@User00159 Год назад

Sir pls do research on vedic maths which will change your life 🇮🇳🇮🇳

@tamajongmichaelnkeh1978 4 года назад

That is the easiest method I have ever used. I can't imagine that I did not know this before. Thank you sir

@luzianleser 4 года назад

Google PQ

@DominicanOps 4 года назад

I think the Colombian Method is easier to be honest.

4 года назад

DominicanOps what Is the colombian method?

@user-wq7dv3vs3p 4 года назад

@ ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-jcRW2R42azE.html

@theunseenblade5897 4 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-tRblwTsX6hQ.html RU-vidrs discovered it years ago

@harisomerbasic9136 4 года назад

My teacher had me explain this to her and now she's recommending your technique and referencing to you! Thanks from Sweden!

@harisomerbasic9136 4 года назад

not your but as a tip

@jackeroo75 4 года назад

Of course other countries know this while USA still wants kids to learn the route method

@muhammadazeem9775 4 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L4ImyFn1xLk.html

@LiveHappy76 2 года назад

@@muhammadazeem9775 Just a tip, based on my personal preference. I almost never click on a video link that does not include a brief statement of what the content/summary of that video is...you'll attract more clicks with a brief statement. Nice rose picture.

@beteilniguse8072 3 года назад

This is exactly how we learned in my country East Africa. God how did I forget this, and our professor has zero clue and got me confused and spent days to really figure this out. I wish I found you early. I would have saved a lot of time. But thank you so much! You did an amazing job. keep them coming.

@geraldillo 4 года назад

Every highschool teacher should learn this method

@rukmaniranganathan8420 4 года назад

Yes

@daisygacha311 4 года назад

True talk

@muhammadazeem9775 4 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L4ImyFn1xLk.html

@chandasubba3502 3 года назад

X²+6x-27=0

@devonyumen8116 3 года назад

No plssss. This is complicated 😭😭 like why can't we just use the quadractic formula. It isn't that difficult to remember 😔

@RavinaTutorial 4 года назад

Sir please keep posting such methods so that people start analyzing mathematics and taste the true essence of it, Thank you so much for sharing this🙏.

@psloh 4 года назад

@espenvang3053 4 года назад

What a marvellous lecture in every way! Not just a genius new method for solving quadratic equations, but also clear and precisely presented.

@creativeclub2023 4 года назад

The Indian mathematician Brahmagupta (597-668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD,[24] but written in words instead of symbols.[25] His solution of the quadratic equation ax2 + bx = c was as follows: "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."

@fyradur 4 года назад

Damn I've never been able to solve quadratic equations with irrational solutions purely in my head but now I can.

@aaditrangnekar 2 года назад

Do your work and find some podophiles not quadratic lol

@part4963 2 года назад

@@aaditrangnekar lmao

@gautamghaisas 2 года назад

I wish we could have learnt all subjects this way in school. So systematically and brilliantly explained

@joebrinson5040 4 года назад

I have never seen this method. Beautiful. Thank you. Retired math teacher.

@psloh 4 года назад

Thank you for your career of teaching!

@muhammadazeem9775 4 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L4ImyFn1xLk.html

@jecelaguilar9319 3 года назад

Haven't you taught your students one of the methods in finding for the roots of a quadratic equations is by completing the perfect square trinomial? This method is used how we arrived at the so-called quadratic formula😀

@chocolateangel8743 3 года назад

@@jecelaguilar9319 At first, I didn't get what he was doing. So, I Completed The Square on a couple of problems, using an area model. I'm a really visual and conceptual math learner, so things like area models really help me. After I did some problems, I realized that his method is basically a shortcut for Completing The Square. I had the idea because he said his method always works. To those of us in the U.S., this approach seems different because it's not the exact way we are taught to Complete The Square in school.

@norbertotorbeso2562 4 года назад

I have been teaching this method to my high school students back in 1999 and yes, this is another way. Students will definitely learn if a teacher will expose them to different ways of solving the problem. Nice presentation...

@geraldillo 3 года назад

I realise that this is basically not much different than completing the square. Why was this method not widespread before? It would have saved many students a whole lot of suffering...

@Latronibus Год назад

@@geraldillo The one thing I don't like about this method relative to completing the square is that it doesn't teach the "add and subtract" trick, which is useful elsewhere in math. To clarify what I mean, I think of completing the square in this kind of format: x^2+2x+2=x^2+2x+1-1+2=(x+1)^2+1. The "I can just put a +1 there as long as I take it away later" concept is kind of magical to an algebra student, but is widely used elsewhere in math. Unfortunately I sometimes see students learning this in terms of adding the desired quantity to both sides of an *equation* which is really the less common way to think about it in more advanced math.

@g.v.3493 4 года назад

I’m reviewing all of my precalculus math that I had 50 years (!) ago. I wish I’d had you for a math teacher back then. Thank you so much for the teaching an old dog a new trick! I’m planning to learn a lot more new tricks. I’ll be watching more of your videos in the future! Thanks so much!!

@muhammedshameel5684 4 года назад

This is why I love mathematics, 😀😀

@muhammadazeem9775 4 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L4ImyFn1xLk.html

@MichaelBuck 2 года назад

Mind Blown! Genious! Not just in the solution but in the expert EXPLAINATION, very clear and understandable, just amazing! Thank you for taking the time to produce this video. I will go over it several times to make sure I understand its simplicity. I am now a follower and will look over your other videos. Wow, just amazing how ancient secrets from hundreds and thousands of years ago are lost over time but come back to life. I wonder how many other things are like this?

@dananewborn8926 2 года назад

Thank you from my 19 person math class who enjoyed learning this method

@blockyboxhead Год назад

I watched this entire video without getting bored or wanting to click off. This proves that this video is godly

@trudyandgeorge 4 года назад

This is so elegant, intuitive, and forces the solver to think about what's happening and how things relate to each other. I wish I had RU-vid back when I was in school.

@gregnixon1296 4 года назад

If there were RU-vid when I was in school, I would never have gone to school. Attendance and tuition would have been a waste of resources.

@carolinebrown7634 3 года назад

VIO stand your life.

@keinKlarname 4 года назад

You're such a friendly person! It's a pleasure to follow your explanations, Mr. Loh.

@sandanadurair5862 2 года назад

You are simply great. I have never seen such a pleasant mathematics teacher during my learning period. I am now 72. Today you taught me a novel technique. I salute you

@wreckim 2 года назад

As a 4th grade teacher, I can tell you that it would be incredible to have this kind of talent exposed to the kids right from 1st grade on. So much of the math problems we have is because we lack our natural curiosity and stop having fun. Math gets to be all about 'testing' pretty quick once they leave 6th grade. Thanks for posting, great lesson.

@jenm1 2 года назад

You could teach them!

@ksamsati5254 4 года назад

What clarity, elegance & humility. Thank you.

@heaslyben Год назад

What a joy that this method fits naturally in each number domain! The intuition of "finding the average" leads so smoothly into creating a complex conjugate pair. It's as if we knew more than we knew we knew, all along. Thanks for sharing this so well!

@edlopez5661 4 года назад

What a great explanation to the how they came up with the quadratic equation. That was the best I've seen in quite a while. Thanks.

@nicolealfonso5225 4 года назад

Thank you so much! I'm studying for the GMAT right now and this method is going to help me work through quant problems involving quadratic equations much more quickly and efficiently!!

@forsadaqah183 4 года назад

Teachers like you and my best maths teachers(Chandan Sir,Azizul Sir)really inspire the students to discover and love the maths.Much respect to every good and ideal teachers.

@KarmaIsEternal 4 года назад

This man is a LEGEND!

@creativeclub2023 4 года назад

@zykorplayz7618 3 года назад

@@creativeclub2023 stfu

@raselalafaele4527 3 года назад

thanks Po-Shen Loh, I never studied this method in school or in University but I'm so thankful for sharing your knowledge and understanding of different methods to solve quadratic equations. I prefer learning this method for all students to know is the best choice than the normal way. Glad how you ended up connecting or even linking to the Quadratic Formula itself.

@explorer2645 4 года назад

Brilliant! Very well explained. I wasn’t aware of this technique before...something different.

@kirilkirilov6241 4 года назад

Great method! It's so rare you see an improvement over such a basic thing as quadratic equations. I just love your enthusiasm. Science Alert brought me here.

@alifmusyaffa9666 2 года назад

I can't believe that im finished watching this video, its amazing how Mr. PO makes math looks very interesting. Respect ❤️

@nagzul1 Год назад

I actually watched the 40:05 minute video without skipping!😂 Just like learning golf, when you can connect with the instructor through the way the knowledge is properly conveyed, then you find gold at the end of the rainbow!🎉😊

@edmund6392 3 года назад

Showed this to my 7 year old math obsessed daughter and she immediately understood. She loves learning advanced math and we love your explanations. Thank you!

@adamholub6436 4 года назад

I am from Czech republic and I know this since elementary school. It's one of the taught methods to solve cuadratic ecuations.

@samvendetta1744 3 года назад

Same in Kenya

@odinmandu2184 4 года назад

What have I been learning all my life🙆🏾‍♀️🙆🏾‍♀️ This is beautiful 🔥🔥🔥

@SuccessTeamEngineeringDesign 4 года назад

This is very helpful. Thank you Dr. Po Shen Loh for expounding our knowledge of maths in a precise way of Reasoning without guessing.

@laurachitez8938 4 года назад

What a wonderful person you are many blessing to you, we need more people like you!

@almightygod1023 4 года назад

This is amazing. This is" MIRACULOUS " that was very kind of you for sharing this. THANKS A LOT

@alisharif3827 3 года назад

Thank you for your fantastic teaching skills. I'm very happy with your lessons, because it's so easy, but I don't know why they don't teach us in College like this beautiful way. Thanks a lot.

@mathyou5436 4 года назад

I really like they way you're emphasising IF -> THEN logic in this video.

@jw5287 2 года назад

love the energy and the great insights, really helped me understand the concept of the formula much better.

@laurenbrock5056 2 года назад

This was amazing! I actually had to pause the video and derive the quadratic formula because I was so excited about noticing how it relates to this method. As soon as I finished I unpaused the video and Professor Loh started talking about how to use the method to derive the quadratic formula. The logical pathway is so satisfying in this video and I am grateful to finally understand the quadratic formula!

@success687 2 года назад

Hi....

@-unnamed-2652 3 года назад

This is actually the pq-Formula, but i never understood how it came to live. Thank you for this illuminating explaination.

@faruqhsj 4 года назад

Brilliant way of solving Quads in a more generalistic manner , for helping our natural brain go straight without much of guessing ! You have illustrated so nicely , with great patience in the interests of diverse learners and practitioners , dear friend in Maths ! Bless you ! 👍❤😍✨

@annakairema6774 3 года назад

Many thanks for this video! It gave me (and my high school students) new insight into understanding the cubic equation formula which uses the same beautiful ideas explained so well in this video. It never crossed my mind to use these ideas to solve the simpler quadratic equation. So, thank you! Best regards, Anna/Helsinki/Finland

@philplante6524 Год назад

The method at 00:46 is just the quadratic formula. - B/2A +- u, where u^2 = B^2/4 - AC. The x-coordinate of the vertex of a parabola is -B/2A. It is also the line of symmetry. If you extend the line of symmetry through the x-axis, you will see that one root is a distance SQRT(B^2 - 4AC) to the right and the other is a distance -SQRT(B^2 - 4AC) to the left. The method is a bit different than just plugging numbers into the quadratic formula, but there is really no new math here, just a different way to apply the quadratic formula.

@mohamedabdou-salami 10 месяцев назад

No new maths but simpler maths 😊

@balagopalm5995 4 года назад

Thank you sir. It's a brilliant way of solving quadratic equations rather than memorising the quadratic formula. Hoping for you to come up with many other tricks to simplify Math

@basalduat 3 года назад

Thank you Po-Shen!!! You are an extraordinary teacher/lecturer.

@moinmalik1320 4 года назад

Dr. Loh: The technique of completing the square and its formal form, the quadratic formula, are beautifully re-interpreted to present an easy to handle method. Will always love to tell my students this method, giving your reference (Dr Poh-Shen Loh) and encouraging them to watch on the RU-vid.

@johankotze42 4 года назад

Dear Prof Loh, I am now retired at 61, and I have worked in IT for most of my working life. I have, however, always dabbled in mathematics. The thrill of discovering this only recently, is one the reasons for my continued love of the subject. If you have not done so, adding the graphical interpretation would help many other students. Thank you very much.

@southernkatrina8161 4 года назад

Could we try it on Desmos?

@johankotze42 4 года назад

@@southernkatrina8161 Desmos?

@southernkatrina8161 4 года назад

Desmos is a free download app that takes a function and graphs it. It's good fun and helps learning.

@chocolateangel8743 3 года назад

I had to find videos that explained it, graphically, in order to fully understand what was going on.

@Josdamale 4 года назад

A brilliant method brilliantly explained. Much appreciated.

@sarahakhtar345 4 года назад

Few weeks before my gcse exams I find you and I love to your vids I'm defo using these methods in my exams thanks sir. I'm subscribing.

@hyekyungkim6850 3 года назад

He is the BEST teacher ever! I loved how he teaching way. Thank you!!

@robertcastillo8157 4 года назад

This is a great way to approach quadratic equations...great job!

@josenoelteh69 4 года назад

Unbelievably easy and effective!!! Wish I knew this when I was a lot younger though he he. Thanks heaps. Cheers.

@senthilkr1970 Год назад

Very interesting and amazingly explained. never imagined i should have seen this 40 min continously without stopping. Great. Love to learn more.

@kathygedamke2167 Год назад

He's actually "completing the square"! Throw the constant on the other side as a negative, take half of b, square that and add it to the number on the other side. Then you take plus or minus the square root, then add the number from the left side. I was actually thinking along those lines a few weeks ago, but didn't have time to follow it through. Hats off to you!

@ericofarias254 4 года назад

Po-Shen Loh's enthusiasm is the best of the video

@mystiseed9443 3 года назад

I have just one word for this "AWESOME"

@jensimaster 3 года назад

This is amazing, I am watching your videos to see if they'd be a good resource for my son who's 14, but you just taught a 43 year old engineer something new! Thank you!

@pamelafrancis4476 3 года назад

Thank you for explaining everything so clearly also for your time and trouble in bringing this to everyone.

@Futurewarrior507 4 года назад

Thankyou for giving us, such a nice method to solve the quadratic equations

@_p0tz_ 4 года назад

Normal methods require quadratic formulas or completing the square. This method combines the two which makes it easier

@M.Ack11 3 года назад

Splitting the middle term is also another normal method to solve Q.E

@huguesl2096 4 года назад

Thank for this clear and excellent video. I will recommend my students watching your video and use your method.

@chinli72 2 года назад

This method is so much simpler than what I was taught. Bravo Prof. Loh!

@cakiilunicorn7929 3 года назад

Can't wait to find this in text books in a few years or so.

@guesswho386 4 года назад

That was absolutely amazing!!!

@esifohawkins4697 Год назад

I like your teaching style. you actually explained how you arrived at a number which a lot of people don't do. Bravo!!!

@harshdeeprandhawa5872 3 года назад

shoutout to people like this on youtube for carrying us through school single-handedly. THANKYOU

@dlu0813 4 года назад

Thanks Mr. Loh! You're a great help to my math career and I can't wait to see more challenge videos! :)

@psloh 4 года назад

Pleasure to share this one with everyone!

@dududaud.4221 4 года назад

Yes..... He is a genius... Thanks Dr. I love Mathematics my favourite

@academia1798 4 года назад

Sir your content is highly discussed by Triangular Kamal which is really easy for all kinds of people. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-CMNDwY7q7AU.html

@mathisreallyfun 4 года назад

Amazing! Will start showing students this too! Thank you!

@psloh 4 года назад

Nice to connect with a fellow educator!

@mathisreallyfun 4 года назад

Po-Shen Loh yes! I’m so happy when I saw your video. Really inspiring! Thank you!

@ramonalejano671 Год назад

Professor Po-Shen Loh found and original insight. You are amazing!

@angelitapascual3695 4 года назад

Thank you so much Sir for an additional know how on solving Quadratic equations in a different way..great to share with others.

@naurnootnoot 3 года назад

This is groundbreaking material, truly eyeopening

@AtunHotepRe 4 года назад

Much Thanks Prof. Loh ... Outstanding!

@pratyaksh1729 3 года назад

Its just the quadratic formula

@davidrossmanith9003 Год назад

This was great. Mostly because you are a talented instructor. You look so happy and proud of this method, and it makes learning it much more engaging. Thanks for a fun watch.

@ravikrpranavam 4 года назад

Thank you, I loved your method, it is easier to get the solutions!

@shenlongslostballs6443 3 года назад

It uses the implication of transitive relation 'if' this exists 'and' the next condition Exists 'then' the third condition must exists to satisfy the relation. Thanks a lot sir for this method it's more solid compared to guessing factors

@michaelsienkaah654 Год назад

You have made me cry

@maarofyusof1883 4 года назад

Ok this is fun. Thank you Mr. Loh for detail explanation

@liss-sanedrac 2 года назад

I’m glad I found this video. I’m sure it’ll help a lot once I get into the more advanced algebra lessons.

@johntaylor181 3 года назад

The brilliance of this method is only rivalled by the excellence of the presentation! WONDERFUL!!

@4theTruthseeker 3 года назад

Seeing this.. i feel like im recovering from my illness... So unreal.. thank you professor.

@tuonglannguyen4012 4 года назад

Thanks professor for very meaningful video, really love the way you express the logic and guide how to produce the result, actually in real use it will be very quick by just writing down neccesary part to calculate. And in fact i learnt 1 new trick of solving sys of equations consists of a product & a sum (the average plus/minus). Also i would like to contribute another approach for this as well: x^2 + bx + c = [x^2 + (2b/2)x + 1/4] + c - 1/4 = (x + 1/2)^2 + c - 1/4 . It's look a bit complicated but if understand how to express (a + b)^2 should be very easy to imagine. But then, just another trick, and the important is still how we understand things and utilize them the right way.

@moukafaslouka4796 3 года назад

Best explanation I have ever seen on this method. Thanks for sharing!

@tusharamreliya5250 3 года назад

Best lecture ever seen on quadratic. Thanks Mr. Loh❤

@ayushmansharma4362 4 года назад

Thank you very much sir for this wonderful method. I m an indian JEE ASPIRANT and even i m very thankful for this method. I really going to share it with my friends.

@anshumanagrawal346 4 года назад

But Isn't It Just Completing The Square?

@ayushmansharma4362 4 года назад

@@anshumanagrawal346 it will come in handy for tricky quartic quadratic equations

@anshumanagrawal346 4 года назад

@@ayushmansharma4362 oh ok thanks

@alastairbateman6365 4 года назад

May I complement Po-Shen-Loh on a brilliant exposition of a bit of basic, fundamental mathematics. A good example of plain honesty, simple truth and easy understanding. I first watched the video a day or so ago and it was only a day later that the penny dropped. As per Leonhard Euler's 'Elements of Algebra' (x-a)(x-b) = x^2 - (a-b)x + ab where as we know a & b are the roots of the quadratic. Taking (a+b)^2 and (a-b)^2 [ i.e. props. 4 & 7 from book 2 of Euclid's 'Elements' ] then expanding and subtracting we get the answer 4ab hence we have (a+b)^2 - (a-b)^2 = 4ab. This is a theorem, prop.8 of book 2 of the 'Elements' and for some unknown reason demoted to a RULE alias 'The Quarter Squares Rule'. After a bit of simplification we end with [(a+b)/2]^2 - [(a-b)/2]^2 = ab. The algorithm given in the video then amounts to [(a+b)/2]^2 - ab = [(a-b)/2]^2 which taking the square root leaves (a-b)/2. So (a/2+b/2+a/2-b/2)=a & (a/2+b/2 -a/2 -[-b/2])=b. It is still highly commendable that the 'QSR' has been derived by another route and has been admirably utilised for the factoring of quadratic equations. What I find a bit astounding and some what sad is that together with the hits on the 3blue1brown and MindYourDecisions videos on the same topic a combined total of around 1,453,000 views no one else seems to have spotted the connection. Finally if we change a & b to x^m & x^n then the answer (ab) becomes x^(m+n) hence all integers raised to a power above the second are the difference of two squares . Further more the bigger the power the more DoS solutions there are for any one integer raised to that power! What does this mean for Fermat's Last Theorem.

@user-xs4qo6bd1m 4 года назад

3blue1brown U link MindYourDecisions U link

@captaincool6268 4 года назад

Amazing this is the best guide i had seen , helps me a lot thanks ;D

@Edwin-ck5ul 4 года назад

You are a big one amongst the biggest. Thanks you for your contribution.

@jacobhouston1655 4 года назад

I’m going to teach this to all my peers at my community college.

@ly_lols 4 года назад

This is the most helpful video i've ever seen

@doomddudc6440 3 года назад

Thank you sir. I guess I am lucky I got to know this. Will like to meet you in future. Very less people are like you and you have a very nice way of speaking. THANK YOU 😃😃😃😃😃

@taulguedi637 2 года назад

Such a beautiful thing that you have done Mr. Po-Shen Loh.

@tanumaybarman8118 3 года назад

Well explained, Sir. Actually this formula is known as Sridharacharya's formula. Sridharacharya was an Indian mathematician, Sanskrit pandit and philosopher. All the students of high schools are taught this. So I have also learnt this in my school days. Thank you, Sir, for making it more familiar to others. I'm feeling proud to be an Indian. Jai Hind. 🙏🙏🙏🙏 en.wikipedia.org/wiki/Sridhara

@sabitabarman2142 3 года назад

You are right.

@gkamesh 2 года назад

Thank you sir for this information. Mr Loh has explained very beautifully also, and I was not aware that Sridharacharya had already discovered it.

@k1775 Год назад

I think he had derived the quadratic formula we generally use, and this simplified version was discovered by the Babylonians.

@jjphenom2831 3 года назад

I am quite surprised that this has not been more widely known. In Germany it is called the pq-Formula (because of x^2+px+q) and it has probably been the most common way it is being taught.

@chocolateangel8743 Год назад

@JJPhenom I'm American. When I was in school, we were just expected to memorize the Quadratic Formula. It was never explained to us. I had never heard of the PQ Formula -- until I heard of the Po-Shen Loh method and began doing research and watching a lot of videos. I think the way the Po-Shen Loh method is presented (especially when done with a graph) makes it easier to understand & makes the formulas make sense.

@jjphenom2831 Год назад

@@chocolateangel8743 I absolutely agree. I was only surprised that this is not necessarily the way it has been taught.

@chocolateangel8743 Год назад

@@jjphenom2831 I think it's because of how generations of math educators have been taught (at least in America). I've talked to a lot, and the idea of learning math on a deeper level, from a more conceptual perspective, is pretty new for us. Back-in-the-day, being good at math just meant that you were good at memorizing algorithms (even if you didn't understand them). Plus, the standards that teachers had to meet in order to teach math were pretty low. When they first raised them, many teachers that had been teaching for years, couldn't pass them. It was a big deal because they also couldn't replace all these teachers. The kids basically got screwed. These teachers were talking about how hard the tests were to pass. So, I asked some professors that had taught at the high school and college levels. They said they weren't that had -- if you understood math. If just tried to get through everything using memorization, you were in trouble.

@jjphenom2831 Год назад

@@chocolateangel8743 Oh I see. That sounds like an interesting shift in approaches. I will be following up on how successful this turns out to be. Here the formula is often applied quite algorithmically and without going very deep into its derivision. I do not know the reason why this is the predominant method of solving quadratic equatiins though. Would be interesting to see a worldwide distribition

@belmer73 4 года назад

I love the way he teaches, how he anticipates future content, let’s viewers know there is a reason for doing something, his enthusiasm.

@psloh 4 года назад

Thank you for sharing your thoughts! Math is about reasoning, not about memorizing. Everything in math can be taught in a way which illuminates the reasons. :)

@belmer73 4 года назад

Po-Shen Loh yes! It’s no good to just memorize. That will be quickly lost. But the ability to explain your way through a concept gives access to so much more.

@psloh 4 года назад

@@belmer73 :)