Descartes Rule of Signs

Рет қаралды 480,235

6 жыл бұрын

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-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 347

@TheOrganicChemistryTutor Жыл бұрын

Next Video: kzfaq.info/get/bejne/fMplrNZltbeRkYE.html Final Exams and Video Playlists: www.video-tutor.net/

@willfest Жыл бұрын

great video

@glowrenaaatv6507 3 жыл бұрын

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

@benramos7131 5 жыл бұрын

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

@jazminaguilar9714 5 жыл бұрын

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 жыл бұрын

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)

@shadowsneaks3392 3 жыл бұрын

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

@bengitman9313 3 жыл бұрын

lol same

@get_going34 2 жыл бұрын

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

@Jamal-pd1tl Жыл бұрын

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.

@jaimecuatepitzi6278 5 жыл бұрын

Yo. You need a medal. Thank you 🙏

@dhanushbearelly427 3 жыл бұрын

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!

@aliahkristhenmendoza8252 3 жыл бұрын

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

@the_criminal_mastermind 2 жыл бұрын

I feel you there

@bap_man2586 2 жыл бұрын

Got mine in bout 10 👁🫦👁

@rafihassan3622 2 жыл бұрын

I'm about 5 hr before 🐸

@GoChelsea-vq1uq 3 ай бұрын

I have about 4 hours before mine

@frankandmike9805 Ай бұрын

3 hours 😂

@georgesadler7830 2 жыл бұрын

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

@renzotoglia 5 жыл бұрын

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

@chloesamson7904 2 жыл бұрын

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

@jonathan1100 5 жыл бұрын

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

@Name-is2bp 4 жыл бұрын

there's 240 now

@hamslider3055 3 жыл бұрын

☹️

@filipborin555 4 жыл бұрын

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

@jen1969 4 жыл бұрын

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.

@patrice942 4 жыл бұрын

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

@POLYNIKEGMAXOUT 3 ай бұрын

These videos definitely come in clutch when you miss class

@ArnavGarg-rl6qh 24 күн бұрын

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

@KEGon13 4 ай бұрын

Best explanation I have heard yet. Thank you

@Thefrenchaccentedseal 6 жыл бұрын

You made it so clear!! The best!!

@sakshiragini360 Жыл бұрын

Such great way to teach!! Hats off.

@vlogwithbrownie 5 жыл бұрын

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

@kuxli5946 Жыл бұрын

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

@nonentity168 11 ай бұрын

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

@mgm8393 4 жыл бұрын

GREAT EXPLANATION! I FINALLY GET IT!

@camilasummers 5 жыл бұрын

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

@sajidzahid4236 4 жыл бұрын

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

@thearticulator8621 2 жыл бұрын

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

@jaya9833 Жыл бұрын

Made everything easy. Thank you!

@hadenpolk4408 3 жыл бұрын

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

@amitvirendra Жыл бұрын

This just clears so much of my confusion thank man

@maribellamcgovern8532 3 жыл бұрын

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

@noahd1144 4 жыл бұрын

This was the best explanation on KZfaq. Thank you.

@madanravuri 4 жыл бұрын

Excellent Explanation sir. Thank you very much ...

@shengkaijiang3062 4 жыл бұрын

This video very helpful, thank you verry much.

@channelnamegoeshere4707 3 жыл бұрын

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

@elizabethrodriguez804 6 жыл бұрын

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

@AJ-et3vf 11 ай бұрын

Great video! Thank you!

@adityadixit9937 2 жыл бұрын

It just clears so many confusions

@cutebunny6335 10 ай бұрын

Very helpful. Thank you.

@maltzu 4 жыл бұрын

this guy is better than my maths teacher wtf

@mahimsterunicorn7948 3 жыл бұрын

Thanks! your vids are so helpful

@mwerensteijn 7 ай бұрын

Thank you! Great explaination

@harveypaulin7991 2 жыл бұрын

Well done...good pace...

@user-wu5zj9dk3q 3 ай бұрын

Thank you this lesson is very helpful

@shanalaus 3 жыл бұрын

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

@benlee5039 3 жыл бұрын

lmao yuhhh, sophomore gang 😂

@rozaremix6656 3 жыл бұрын

Same

@littlemacmain5117 3 жыл бұрын

Same

@cheshire__kat 3 жыл бұрын

Ifkr I'm d y i n g

@kisracora9676 3 жыл бұрын

x_x brain hurt

@Ramen_Sensei 4 жыл бұрын

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

@TheKatiecat68 6 жыл бұрын

thank you so much!!

@cecileramos1077 9 ай бұрын

Thanks so much ! Keep up your good work😊

@solofelangdikate1410 3 жыл бұрын

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

@catalinaalvarez5919 2 жыл бұрын

thank you sir .God bless from Phillipines

@ngocbui2928 Жыл бұрын

tkssss so much, its helpful a lots

@kylerprice5651 5 жыл бұрын

This is so helpful, thank you so much

@ArnavGarg-rl6qh 24 күн бұрын

Sup dude how you doing?

@gabby6787 4 жыл бұрын

Thanks a lot! 💕

@amannindra6488 Жыл бұрын

THANK YOU SO MUCH

@agrimmittal Жыл бұрын

Thanks a lot dude!

@renatashe 3 жыл бұрын

Thank you, soooo much!!!!

@adityasinha8702 Ай бұрын

dude, you are like the jack of all trades!

@glueissticky9275 3 жыл бұрын

thanks for helping me complete my hw

@ahnjoseph6875 3 жыл бұрын

you literally saved my life.

@ELVISDUMISANI 2 ай бұрын

thank u sir ,you have saved me indeed.

@luckyyanez6362 6 жыл бұрын

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

@yamsang0__0 4 жыл бұрын

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

@Dave-dw2dn 3 жыл бұрын

props to this guy for actually explaining shit unlike my teacher

@jagritipathak8443 4 жыл бұрын

How to find roots of the equation with quadratic,linear and log terms ?

@abdikadirmoallim1268 3 жыл бұрын

Thank you very much really pleased me

@emilyjohnson2544 3 жыл бұрын

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

@the_criminal_mastermind 2 жыл бұрын

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

@uttkarshtewari2532 2 жыл бұрын

u taking algebra 2 in 6th grade? damn

@emilyjohnson2544 2 жыл бұрын

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

@uttkarshtewari2532 2 жыл бұрын

@@emilyjohnson2544 wow gl in high school

@jaedenk999 Жыл бұрын

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

@zhongxiancheng4670 3 жыл бұрын

I'm just cramming before a math competition.

@vijayvyas5075 5 жыл бұрын

Lovely video

@luckyyanez6362 6 жыл бұрын

Thanks!

@ianvillaluz8279 3 жыл бұрын

You’re a legend

@mrchen.4543 2 жыл бұрын

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

@kenkenrednalloh2490 5 жыл бұрын

Thank u sooo much

@selatsera2875 3 жыл бұрын

Thank you vv much! :DD

@gregnoroian3151 Жыл бұрын

Thank you

@Chandangiri8134 Жыл бұрын

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

@AYUSH86684 4 жыл бұрын

loved it....

@hamslider3055 3 жыл бұрын

THANK YOU

@elifarmer3815 3 жыл бұрын

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 2 жыл бұрын

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

@valeriazamora8052 Жыл бұрын

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.🥹😁

@multigamer1213 Жыл бұрын

TYSM

@jonascastejon5888 4 жыл бұрын

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 жыл бұрын

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

@chunkymilk1288 3 жыл бұрын

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

@ii7267 3 жыл бұрын

Thanks

@ComsianMathAcademy 2 жыл бұрын

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

@rammaddirala6857 2 жыл бұрын

This man deserves a free pass to heaven for the number students he saved from failing their classes.

@franchothings819 3 жыл бұрын

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)

@k1ttyang3l 2 жыл бұрын

bruh my teacher literally just reads what's on the screen and i can't understand a thing now she wants us to answer it like we all understood what she said.

@priyadharshiniduraipandi3260 3 жыл бұрын

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

@jericcolumbino1421 3 жыл бұрын

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

@noodlewhitley 2 жыл бұрын

Crystal clear

@munshifahimuzzaman9990 5 жыл бұрын

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

@ayasuniverse 4 жыл бұрын

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 жыл бұрын

To predict our answers and make sure the roots are correct

@010.gutierrezdarylljamesd.7 3 жыл бұрын

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 3 жыл бұрын

@@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 3 жыл бұрын

@@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.

@sudarshanraj168 Жыл бұрын

Thankyou sir

@jcabounce4858 2 жыл бұрын

The factoring part in the last example, what does i mean???

@kaxiku 2 жыл бұрын

@chicanalex4529 2 жыл бұрын

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

@gontsekganyago4079 2 жыл бұрын

brilliant

@ishitaroy7778 5 жыл бұрын

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