Descartes Rule of Signs

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This precalculus video tutorial provides a basic introduction into descartes rule of signs which determines the nature and number of the solutions to a polynomial equation. The number of sign changes in f(x) is related to the number of positive real zeros and the number of sign changes in f(-x) is related to the number of negative real zeros. The imaginary solutions is the difference between the degree of the polynomial and the sum of real zeros including positive real zeros and negative real zeros. This video explains the results of descartes rule of signs using a table. This video explains how to identify the exact number of positive and negative real zeros by actually finding all the zeros of the polynomial function by factoring by grouping and by factoring using synthetic division. This video contains plenty of examples and practice problems.
Introduction to Polynomials:
• Polynomials - Classify...
Polynomials - Basic Operations:
• Polynomials - Adding, ...
Dividing Polynomials By Monomials:
• Dividing Polynomials B...
How To Graph Polynomial Functions:
• How To Graph Polynomia...
Intermediate Value Theorem:
• Intermediate Value The...
_____________________________________
Long Division - Polynomials:
• Long Division With Pol...
Polynomial Long Division - More Examples:
• Polynomials - Long Di...
Synthetic Division of Polynomials:
• Synthetic Division of ...
Remainder Theorem & Synthetic Division:
• Remainder Theorem and ...
Factor Theorem & Synthetic Division:
• Factor Theorem and Syn...
Rational Zero Theorem:
• Finding All Zeros of a...
______________________________________
Real & Imaginary Solutions - Polynomials:
• How To Find The Real &...
Solving Polynomial Equations - Synthetic D:
• Solving Polynomial Equ...
Solving Polynomial Equations With Excel:
• Solving Polynomial Equ...
Writing Polynomial Functions Given Zeros:
• Writing Polynomial Fun...
Solving Polynomial Inequalities:
• Solving Polynomial Ine...
_____________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

Опубликовано:

16 окт 2024

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Комментарии : 359

@TheOrganicChemistryTutor Год назад

Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Fd5ys4PQ-aM.html Final Exams and Video Playlists: www.video-tutor.net/

@willfest Год назад

great video

@syedowaisali2502 Месяц назад

You could factorize the second equation: x^4 (x - 3) + 3x^2 (x - 3) - 4 (x - 3) = (x - 3) (x^4 + 3x^2 - 4). You get one solution x = 3 and others will be 1, -1, 2i and -2i from the biquadratic equation taking x^2 = y and solve using shridharacharya formula. (x^2)^2 + 3(x^2) - 4 where x^2 = y so, it's y^2 + 3y - 4.

@glowrenaaatv6507 3 года назад

honestly, i did not understand descartes rule of signs for my precalc class until this video... you explained it wayyyyy easier than so many others

@jazminaguilar9714 5 лет назад

Thank you so much, I finally understand it. My teacher took 5 minutes to explain this and tbh I didn’t give her my full attention but she then told us to do the next 5 questions and we never even went over it so I was so confused. Not anymore 🤠🤠

@skymango1697 3 года назад

Just wanna point out that this thing actually helped me in understanding the Rule of Signs. Although I'm really a good student in terms of maths, sometimes I go into roadblocks, and when I do, I refer to your channel to see where I missed. So far, you really had a good time explaining this! Thank you very much for this, and please continue doing the things that you love the most (helping other people understand maths)

@ArnavGarg-rl6qh 3 месяца назад

So many concepts in a single video wow your videos are awesome your a life saver thank you

@benramos7131 5 лет назад

Can you begin to imagine what this cat scored on his SAT?

@jaimecuatepitzi6278 6 лет назад

Yo. You need a medal. Thank you 🙏

@dhanushbearelly427 3 года назад

Thanks so much dude, you're like a legend among high school math students. Thanks so much for making this video. It literally helped so much. Thx!

@shadowsneaks3392 3 года назад

this man just saved me from failing algebra 2. absolutely legendary

@bengitman9313 3 года назад

lol same

@get_going34 2 года назад

It's literally 2AM and I'm here... Finally understood this.... Unbelievable!

@Jamal-pd1tl Год назад

I just wanted to thank you for the helpful tutorial you posted on Descartes rule of signs. I was struggling to understand the rule, but your tutorial made it really clear. I especially appreciate the way you explained the different cases and how to apply the rule.

@renzotoglia 5 лет назад

That was complex on the first take. You moved slow and it made sense. Though practice is needed to let it all burn in. Thank you

@husseinalhadi5471 2 месяца назад

Your were extremely thorough and your explanations were excellent!!

@filipborin555 5 лет назад

On 12:23 we can factor by grouping cuz the each two groups of therms are with the same coefficient's ratio.

@georgesadler7830 2 года назад

MR. Organic Chemistry Tutor, thank for an awesome introduction to Descartes Rule of Signs in old fashion precalculus.

@KEGon13 6 месяцев назад

Best explanation I have heard yet. Thank you

@kuxli5946 Год назад

My finals are tmrw you made everything clear for me I appreciate that thanks

@aliahkristhenmendoza8252 3 года назад

Me watching this 20 mins before my exam starts: 👁👄👁

@the_criminal_mastermind 3 года назад

I feel you there

@bap_man2586 2 года назад

Got mine in bout 10 👁🫦👁

@rafihassan3622 2 года назад

I'm about 5 hr before 🐸

@GoChelsea-vq1uq 5 месяцев назад

I have about 4 hours before mine

@frankandmike9805 4 месяца назад

3 hours 😂

@jen1969 4 года назад

You are helping to so much to review polynomials. I was thriving since I transported school and missed this chapter. I was finally going over them a week before the school starts and I feel like I mastered how to solve polynomials from all your videos. Thank you so so much. Also, maybe a video with conjugate root theorem might help more students cuz it's always together with these.

@noahd1144 4 года назад

This was the best explanation on RU-vid. Thank you.

@shanalaus 4 года назад

When most of the comments are college students then me being a 10th grader here be like: * ._. *

@benlee5039 4 года назад

lmao yuhhh, sophomore gang 😂

@rozaremix6656 4 года назад

Same

@littlemacmain5117 4 года назад

Same

@cheshire__kat 4 года назад

Ifkr I'm d y i n g

@kisracora9676 4 года назад

x_x brain hurt

@chloesamson7904 2 года назад

When you thought you already get it but then when the video is nearing to end my mind goes brzzttt😃

@nonentity168 Год назад

Thank you so much. You're such an incredible narrator.

@hadenpolk4408 4 года назад

God bless you man, you teach so good. You saved me

@patrice942 4 года назад

Thank You very much. You have lessened my headache trying to understand this stuff.

@emilyjohnson2544 3 года назад

Thank you so much! I am in 6th grade and really needed this!

@the_criminal_mastermind 3 года назад

You were learning this in 6th grade I'm learning this in college and it's confusing for me

@uttkarshtewari2532 3 года назад

u taking algebra 2 in 6th grade? damn

@emilyjohnson2544 3 года назад

@@uttkarshtewari2532 lol thanks! Now I'm in 7th and doing precalc

@uttkarshtewari2532 3 года назад

@@emilyjohnson2544 wow gl in high school

@jaedenk999 2 года назад

@@emilyjohnson2544 gawd damn i'm just learning this rn in 10th grade

@maribellamcgovern8532 3 года назад

Bro you just helped me pass my Math 151 final, thank you my dude😊

@jonathan1100 6 лет назад

When you realize this guy has *194+* precal classes alone (silently hits subscribe)

@Name-is2bp 4 года назад

there's 240 now

@hamslider3055 3 года назад

☹️

@amitvirendra Год назад

This just clears so much of my confusion thank man

@thearticulator8621 2 года назад

Bro's teaching on Valentine's Day. What a legend.

@FutureDrLee 29 дней назад

Thank you for breaking this down so easy ❤

@POLYNIKEGMAXOUT 6 месяцев назад

These videos definitely come in clutch when you miss class

@sakshiragini360 2 года назад

Such great way to teach!! Hats off.

@camilasummers 5 лет назад

amazing video ... thank you sooo much.... I have a test tomorrow and you literally saved me :)

@sajidzahid4236 4 года назад

Bro thank you so much, I actually understand this stuff now.

@Thefrenchaccentedseal 6 лет назад

You made it so clear!! The best!!

@munshifahimuzzaman9990 5 лет назад

what is the utility of this rule if we actually have to find the roots ?

@ayasuniverse 4 года назад

Maybe tovmake sure that our roots our correct, for instance if we said first that we'll have for example 3 positive roots and two imaginary ones, and after solving we have (for example 4 postive roots) than we'll conclude we made a mistake

@ayasuniverse 4 года назад

To predict our answers and make sure the roots are correct

@010.gutierrezdarylljamesd.7 4 года назад

Descartes' rule of signs will narrow or lessen the number of choices of possible zeros when we are doing trial and error, by knowing how many negative , positive, or imaginary zeros that can be there, we will not waste our time finding more negative or positive zeros than how many it should be.

@ColombianThunder 4 года назад

@@010.gutierrezdarylljamesd.7 Really? I don't see it that way at all. It should be pointed out that I'm also very retarded but i digress. If i see that there are 18 possible zeros, and use Descarte's rule to find out that out of those 18, 4 of them are either positive or imaginary, then i still have to shoot in the dark 18 positive numbers to narrow it down, which to me is incredibly tedious. Of course i won't literally have to try them all, and with intuition you can guess which ones it won't be, but still. I hate it. Is there really no other way except this foggy (though with a slightly clearer path) trial and error? Would figuring out a better way be a mathematical breakthrough or has it been figured out this is the only way? Or is a better solution taught later on but requires more difficult concepts?

@duanedungee5555 4 года назад

@@ColombianThunder 18 possible rational zeros? 18 possible zeros period,? (which suggests an 18th degree polynomial) What degree polynomial function are you dealing with? Newton's Method of approximation of zeros may help eliminate some choices if your function is a polynomial (i.e does not oscillate uncontrollably). You learn that in Calc I.

@adityadixit9937 2 года назад

It just clears so many confusions

@channelnamegoeshere4707 4 года назад

You just saved me my pre calculus when nobody else (Especially not my workbook) explained it well My book basically just said, "Hey here's math there's probably a way to do it but we aren't going to tell you, go" you've earned a like

@adityasinha8702 3 месяца назад

dude, you are like the jack of all trades!

@amannindra6488 Год назад

THANK YOU SO MUCH

@mrchen.4543 3 года назад

I know we are all thinking it, his Ss' are very sharp. To fix this you can add a "DeEsser" to your audio in a video editing program. Or you could get a popfilter for your microphone

@catalinaalvarez5919 2 года назад

thank you sir .God bless from Phillipines

@vlogwithbrownie 5 лет назад

Thank you! This helped me understand how to find imaginary zeros 😁

@DarioVidili Месяц назад

This guy and Brian are carrying my Pre-Calc grade.

@madanravuri 4 года назад

Excellent Explanation sir. Thank you very much ...

@jonascastejon5888 4 года назад

8:35 it's the other way around. Odd exp=no change whatever the sign of x, even exp=changes to positive if x is negative.

@2b2c1d2 2 года назад

Nope because odd number changes the sign like -5*-5 = 25 but -5*-5*-5=-125 don't look at the numbers but the sign instead so odd exp change the sign and even exp don't change sign

@glueissticky9275 3 года назад

thanks for helping me complete my hw

@mgm8393 5 лет назад

GREAT EXPLANATION! I FINALLY GET IT!

@jericcolumbino1421 3 года назад

Hello sir. I just want to ask something. What program are you using for writing in this video?

@jaya9833 2 года назад

Made everything easy. Thank you!

@yamsang0__0 5 лет назад

when its imaginary, the conjugate is also a root right? assuming all coefficients are real and rational

@DarkmarkKitireng 6 месяцев назад

Thank you this lesson is very helpful

@gregnoroian3151 Год назад

Thank you

@franchothings819 3 года назад

based from all of your examples all roots from negative are 1 what if its more than 1 like 3? How would you create the table? example: degree = 7 (+): 4, 2 0 (-): 3,1,0 ::: (+, -, i) does the possible combination follows a plain decreasing pattern? (4,3,0) (2,1,4) ? or nCr table? (4,3,0) (2,3,2) (0,3,4) (4,1,2) (2,1,4) (0,1,6) (4,0,3) (2,0,5) (0,0,7)

@karlavillanueva2493 3 месяца назад

For the first one I’m not understanding how the positive zeros could be 2 or 0 and how the negative could only be 1? Could someone explain the positive integer thing i think that’s what I’m stuck on.

@ahnjoseph6875 3 года назад

you literally saved my life.

@cecileramos1077 11 месяцев назад

Thanks so much ! Keep up your good work😊

@AJ-et3vf Год назад

Great video! Thank you!

@shengkaijiang3062 4 года назад

This video very helpful, thank you verry much.

@mwerensteijn 9 месяцев назад

Thank you! Great explaination

@ianvillaluz8279 3 года назад

You’re a legend

@maltzu 5 лет назад

this guy is better than my maths teacher wtf

@ELVISDUMISANI 5 месяцев назад

thank u sir ,you have saved me indeed.

@cutebunny6335 Год назад

Very helpful. Thank you.

@ComsianMathAcademy 2 года назад

Tell about 2x^2+x+5 How many positive or negative or complex roots exist?

@harveypaulin7991 2 года назад

Well done...good pace...

@valeriazamora8052 2 года назад

I love this guy his videos always help me all my classes .. in chemistry and math last year, and even physics (and math again) this year.🥹😁

@mahimsterunicorn7948 3 года назад

Thanks! your vids are so helpful

@ngocbui2928 Год назад

tkssss so much, its helpful a lots

@elifarmer3815 4 года назад

Very helpful video. I have a question though: Is it necessary to directly plug in a factor (the possible root) to the original equation, since you still have to test it again using synthetic division? Thanks

@andrewkennedy1264 3 года назад

No my teacher taught us to test the possible zeros using synthetic division

@priyadharshiniduraipandi3260 4 года назад

Thanks for teaching but I have a one doubt sir ... Positive negative First line it's easy to taken but 2nd how to take ? Pls explain

@rahulkankariya14 2 года назад

At which level this is taught? I have never learn before or heard before?? About Descartes rule

@Ramen_Sensei 4 года назад

This helped me so much!!!!!! Than You!!!!!

@chunkymilk1288 3 года назад

I'm so happy this man won't let me fail 8th grade :D

@shangjiang3320 2 года назад

Quick question : IXL taught me that you can add or subtract the amount of roots to get different amounts of roots For example, if you have a cubic function, that could have 1 negative zero, then you can say it also could have 3 negative 0’s

@shangjiang3320 2 года назад

So in the first problem, didn’t you miss the case where there are 3 negative zero’s?

@bobbyno93 11 месяцев назад

@@shangjiang3320you can only subtract by 2 and you cannot go below 0.

@solofelangdikate1410 3 года назад

You helped me a lot.thank you....

@agrimmittal Год назад

Thanks a lot dude!

@sarcadistic9762 5 лет назад

What if the coefficient of a variable was 0? Would that be positive or negative?

@kentnaputo7963 5 лет назад

It is depending on the sign to the left if there is a minus its negative an if there is a plus sign its positive

@aoifepeterson6972 5 лет назад

If the coefficient were 0 that would mean there is no term, so you just skip that one. For instance: 2x^3 - 0x^2 - 4x + 3 Since anything and everything multiplied by 0 is 0 the 0x^2 term would equal 0 so you can leave it out. You end up just needing the answer for 2x^3 - 4x +3. Does this help a bit?

@Premium55 Год назад

@@aoifepeterson6972yes thx😮

@elizabethrodriguez804 6 лет назад

This is very helpful! Great explanation and organized. Thank you a bunch :))

@luckyyanez6362 6 лет назад

Bro, can u discuss also about complex numbers and demoivre's theorem? We tackled that before but theres still things I can't answer. If possible do u also discuss calculator techniqe? Hope u can using 991ES or 570ES. It would be a great help. Thanks

@powerdriller4124 8 месяцев назад

Just feed the coefficients to a number crunching polynomial root finder softwate (like online Wolfram), and forget about Descartes Rule. Not to say that polynomial equations in real engineering are gonna look like: x^3 + 3.1567 x^2 - 0.198x + 45.934 = 0 No way for guesses with nice single digit integer numbers.

@Chandangiri8134 Год назад

Sir, please explain why you subtract 2 everywhere when the variation of sign in the sequence of the coefficient

@AnshuKumar-oj8ww 4 года назад

One way to avoid using synthetic division way is - x^5 - 3x^4 + 3x^3 - 9x^2 - 4x + 12 = 0 x^4(x-3) + 3x^2(x-3) -4(x-3) = 0 (x-3)(x^4 + 3x^2 - 4) = 0 (x-3)(x^4 + 4x^2 - x^2 -4) = 0 (x-3)(x^2(x^2+4)-1(x^2+1)) = 0 (x-3)(x^2-1)(x^2+4) = 0 So x= 3,1,-1, 2i,-2i So 2 positive ,1 negative, 2 imaginary

@kylerprice5651 5 лет назад

This is so helpful, thank you so much

@ArnavGarg-rl6qh 3 месяца назад

Sup dude how you doing?

@prod.winterxphool6227 3 года назад

Hey man, Question. Why doesn't the sign change when its even? I thought normally a number like -1^2 = +1 and not -1

@renatashe 3 года назад

Thank you, soooo much!!!!

@abdikadirmoallim1268 3 года назад

Thank you very much really pleased me

@usmanamini1871 4 года назад

Please tell me how you find the x=1 is f(1)=0 . you said something about possible factors of 12 and then possible factors of coefficient of X^5?? do you have any Video about this? if yes please tell me the Adresse

@chicanalex4529 3 года назад

In the first example, is the total 3 because it is the biggest polynomial?

@ryananthonyfernandez4674 3 года назад

Shawn Mendes is teaching Math now?

@TheKatiecat68 6 лет назад

thank you so much!!

@theawesomejoram3873 5 лет назад

i was so satisfied you fixed that line (7:16) that really relieve my OCD there thanks hehehe.....

@Dave-dw2dn 4 года назад

props to this guy for actually explaining shit unlike my teacher

@benoitbarbier5017 3 года назад

Thanks!

@noodlewhitley 2 года назад

Crystal clear

@ishitaroy7778 5 лет назад

Sir I have a doubt in case of +ve and-ve the 2nd step that is 2-2=0 and also that in case of -ve block that is 1 & 1 in both 1st and 2nd step how it had just came if u plz clear it out once again

@hamslider3055 3 года назад

THANK YOU