Descartes' Rule of Signs

[zumbaluv87]

I take an online math class and some things are hard to teach myself in print. This helped me a ton! Wish I would have found it 2 hours ago when I started this problem!

[patrickJMT]

@zumbaluv87 come back any time :)

[Naturally101]

Thanks :)

[zanedvs]

your hairy arms are very distracting

[BallpenEater]

@zanedvs If you're commenting about his arms, then you're obviously not watching selectively.

[TheVare0015]

lol there was a commercial in the middle of the video where the host of the biggest loser gave us "cat tips" which encouraged us to set aside 10 minutes a day to play with your cat, so it gets exercise. 1) i hope cats get more than 10 minutes of play time a day. 2) now we have to be concerned with feline obesity, too? 3) this is unrelated to your vid, sorry. 4) i love your channel.

[indiyannajones]

thanks for saving my butt for my test in 15 mins! YOUR MY HERO!

[devinekralc]

What my teacher taught me as far as the P(-x) and finding the number of times the sign changes is you can just look at the odd exponents like 2x^5 and -3x and change their signs, so it would me -2x^5 and 3x. But over all this video explained this concept better than my teacher. thank you :)

[Lucerozeus]

thx this will come in handy on tomorrow's test

[patrickJMT]

@Lucerozeus good luck!

[EpicRPGRemixes]

Hey, you're left-handed like me! :D

Thanks for the vid!

[bravething2011]

thank so much sir!!

[alphamale442]

Hmm, I think I can apply that basic concept to finding the nature of the roots, however there's only 1 sign change which is at the front of the first variable.

[xHaruu]

Thanks OTL you are more helpful than my teacher who loves to shortcut her lessons based on a bunch of books.

[Tormentlove1]

لقد ضقت ذرعا لم أفهم شيئا

[paagera]

its well explained here, but i have a question that is actually asking me to discuss the zeros after applying the descaretes' rule

-x^5 + 2x^4 - x^2 -1

ive spent so much time on it, yet i cant seem to be able to solve it

[HeIsTheStig]

Thank you, so much :,D

You are an inspiration to us all!

I am definitely sharing your videos with my classmates tomorrow, right after acing my last test of the semester! (Hopefully)

[patrickJMT]

@HeIsTheStig thanks for sharing with your friends!

[illuvitar]

thanks. made this much easier than my book did

[IdiosoAmericano]

Bro I love you

[pyao256]

Thank you so much OTL

[oat1000]

:O You are teaching robots as-well! I hear the robot translator in the background.

[xxweirdwonderxx]

Why didn't I look this up before I failed my test -_-

[systemsteven]

what school do these people go to where they learn this stuff in 2 days?!

[sackTizzle]

you didnt cover imaginary solutions...

[patrickJMT]

@sackTizzle neither did you

[maiithri110]

please let me know how x=0 here....its eating my head

[BallpenEater]

@patrickJMT  Owned. =))

[newbballer1]

wow, why cant math teachers just teach like this?? so simple and yet it is so easy to understand... i learned a 2 day lesson in 12 minutes :D THANK YOU SIR!! u deserve an award!!!

[garryri2002]

wah thank you so much!!!!

[19912010ahcWoodburn]

Thank you! I'm pulling a all nighter and this was really helpful :)

[patrickJMT]

@19912010ahcWoodburn my pleasure : )

[shiftkeyk]

Thank you so much for this!

[patrickJMT]

@shiftkeyk yep, you are very welcome

[J2DaPhizzle]

This was pretty helpful.

[smearedx13]

omggg thank you!!!!!!! i learned more from this video than in two days in class

[esiruno]

the total number of roots are equal to the highest degree of exponent right? so for example we're done with finding the positive and negative roots of the equation but it is still less than the total number of roots, does it mean that the remaining roots are complex numbers?

[tska84]

so since there has to be 1 real negative root and there are 2 or 0 real positive roots does that mean there has to be 2 or 4 complex roots, because its a fifth degree polynomial?

[khashya786786]

@patrickJMT ..isnt 1 a multiple of 2..soryy if that's a dumb question :(

[patrickJMT]

@khashya786786 no, but 2 is a multiple of 1 !

[thaoplayer]

Thank you! you save me from failing my quiz!

[Metallica1554]

I don't understand the last part, how do you know there are some complex solutions?

[thatoneguymusic1]

@Metallica1554 Because there is are 5 roots (excluding the 0). One for each degree of the polynomial, learned that in Algebra 2.

[tiff4annie]

for change of signs, let's say I have a max of 3 real postive roots, does that mean i can have just have ONE (3-1) real postitive root too?

[Sturmdude]

screw the hawkes learning system, that program sucks, I'll just go to youtube.

[lukntomyeyes]

thank you so much for uploading this..means a lot .. :)

[joshpriebe1234]

thanks, it really helps stuff i learn in my online class make sense

[flamaccent122]

Thank you so much for these videos, man. I have a huge test tomorrow, and these videos really helped me out a lot. thanks again!

[ovvvvvvvvrz]

Cogito, ergo sum

[shylerlove09]

In my math class we have to do a chart where we lable the positive, negative and complex... i am having problems filling out the chart correctly! help please!!

[crazyboy58]

thank you so much

[DesecratedReaper]

holy shit thx, also nice hairy man arms

[BugJasmine]

Thank you so much![:

It's amazing how so many people just give up in classes because they don't understand.

Whether I have missed a class, was not paying attention, or just didn't understand, I always come on youtube and search.

Helped me alot! Thanks again[:

[patrickJMT]

@BugJasmine my pleasure ; )

[SuckMyUke]

12 min of youtube= 60 min in a math class

[TypicalGuitarGuy]

-daddy! daddy!- the son screamed with joy - How do you know so much stuff? Your a genius daddy!

-Oh please my son, its nothing... - he said modestly

-But daddy, you fixed the car without being a mechanic; fixed the fridge without knowing anything about it, you explained advanced physics to the teachers at school, YOU built a rocket ship and went camping to mars ! You are the best daddy!

- Oh my son, Thank YouTube- :)

no son, i didnt go to school. At my times, YouTube existed. :)

[ciroccostones]

Thank you so much :D

[MakedaLov]

Thank You!! :D

[ThatOTAKU]

Amazing, for the 1 week I've been trying to learn this in class, you did it in 12 minutes.

[LifeAmongTheDeadBand]

WOW! Thank you so incredibly much! I didn't understand this before your video but this is soooo easy now that I see it! THANK YOU!

[DaisyLech]

You are awesome!!! Thank you for the reference!!

[NVB1035]

Hello,

We really enjoyed your video! We watched it at night (instead of listening to our teacher teach). Though we thought you misspoke a couple times, it was an invigorating experience overall. Hit me up at mathnerdzz.c o m. My user name is Randy1224. Hope to hear from you soon.

-Nikhil and Tommy, Age 12, Dedham, MA

(original message credits to zoebo123)

[MissSmith21]

This was really helpful. I actually missed this part in class the other day and I'm so glad that people like you give people like me free help by making videos like this. I have a take home exam that's due at 8am!

[toolbass24]

Thank you man

[son1ong]

thanks

[tonyplaneslpt]

thank you man. very helpful

[timesente]

@patrickJMT

I have a question, my textbook fails to put emphasis on needing to have a constant term when using this rule, however I noticed at 10:27 when counting the sign changes of the factored polynomial compared to the un-factored one at the top is still 1.

Coincidence?

[Z4d1s]

YOU. Are a god.

Thank you for teaching me.

[rynoweston]

Thanks man. I need to re-watch this a couple hundred times before it sets in.

[timesente]

@rynoweston

lmao same here man

[meluvfood4lifexd]

Why can't you be my math teacher instead? :(

This shows how crappy my teacher teaches.

[SuzieQ1046]

So is it really sad that I learn math a billion times better from watching these videos than I do in my math class?

[patrickJMT]

@SuzieQ1046 no, why would it be?

[berserkace]

@patrickJMT honestly you're waaayyy better than my university precalculus 1 teacher

[tonydeadlock]

@patrickJMT because we get up and go to school to try and learn this stuff and it does not work. We watch your vids and we learn for free your better then college

[TheDancarr60]

you are the man

[patrickJMT]

@TheDancarr60 i am the dude. (big lebowski)

[bmtbebe001]

ur the man!! ty so much

[omarg123456]

wow this is really helpful!

[vietnamesegalz]

almost all math people are left handed, why?

[strayS2K]

@vietnamesegalz I thought it was odd too...until i realized all of the videos I was watching were by Patrick lol....He's the man.

[nomonomo179]

@vietnamesegalz well not all

[louryder33]

one question for positive real roots, for example you get 2 positive real roots and Zero. I understand how you get zero because of imaginary numbers, but the exmaple where you got only 1 real root at 9:11 , how come you dont get zero real roots too. Is it because the power is odd and not even? please post back by tom, i have a test l0l

[freddw1]

awesome, how do we figure out what the roots are?

[fernandoarrue87]

@freddw1 By factoring, quadratic formula, etc. It depends on the particular polynomial.

[Divide]

Thanks for all your great videos!

[DarkHorse610]

PatrickJMT is the best thing since sliced bread, running water, and pockets on pants. Almost as good as indoor outhouses, but not quite. Good looking out, I'm passing because of you!

[ThisComputerGirl]

omg thank you I was so confused with that how they were getting those numbers.

[ashnabwa7d]

your the best :)! thanks

[LAO90]

no sence at all

[ReneePhelan]

THANKS IT MAKES SENSE NOW!!!!!!!!

[bononcrusher2]

so wait, what about the x=0, that won't be counted anymore? This is for a report so I need an answer ASAP.

[RespectMyHate]

Youtubes my new math teacher.

[charlatte008]

i agree. sooo helpful. but don't u think the bright light your using makes your arm look freakishly skinny XD

[marelina92]

Woah thank you soo much this really helped me understand this topic, u did a very well job teaching :)

[TheBlackLesbian]

thanks, i have a final exam today with this :)

[sarahstarr100]

Thank you so much. You are saving me 20 dollars an hour on a tutor. You are really helping me with my college algebra class.

[tholloway2]

You have and are helping me through my college Algebra class! You are a wonderful teacher!!!

[YOURFACEBIG]

Thanks so Much! I didn't understand when my ALgebra 2 teacher was teaching.

[witeflight]

I have only 50 min of class time with my professor per week, and I share that with 300 kids. These videos are so much more effective.

[Hamtheruleroverall]

Thank you so much for doing this, my teacher and text book were of no help to me when trying to learn this subject matter.

[enigma887]

thankyou so so much for taking your time to create this!

[weezerpinkerton]

That helped a ton thanks! But how do you find how many negative zeros you have?

[Misslovefly]

What was the guy tripping on when he figured this stuff out? Any who, thanks for the explanation it's really helping me with my class.

[TheGhostOfSasquatch]

Thank you so much...my teacher at school isn't the best so it's hard to understand what he's talking about but you are amazing at teaching!

[212trooper]

same with our teacher :/

[stuckosu8]

Extremely helpful. Thanks

[logotgr]

Thanks so much. This was one particular thing that I didn't understand in class but I get it now.

[iibxflankin]

dude i gave up till i saw ur tutorial god bless u, i felt lost in class

[mgonzalez7123]

thank you!. I get it now!

[german0809]

I am really glad I found your lesson.

I just started my hw on this topic.

It is really helpful.

keep making this kind of videos.

thanks.

-German G.

[cherrygoldprincess]

u make this so easy to understand. in my algebra class i feel like im on another planet cause i dont understand a thing my teacher says...that and the fact she's always absent..

Thank u Soooo much!!!!

[BaronsBoi]

perfect.. well almost... what about the imaginary roots...

[africanpearl03]

they always come in pairs! for example u can't have i by itself withou -i

[hapeningirl]

thank you sooo much! I've been reviewing this for the past hour and the book didn't explain the decrease by 2... I know I'll do well now :D

[gorillaz117]

HELL YEAH PATRICK U DA MAN!!! if it wasn't for you i would of completely failed my bi-mester final exam but you helped me get a perfect !!! thx man keep up the good work with the videos : )

[strikedeathscythe]

wow thank you, my teacher cant teach =/

[pearl6394]

How do you find possible imaginary solutions?

[MrPizzaboy117]

Hay im not the maker of this vid but we did go over this in calss. ok first of all you know that you can finde the total number of roots by looking at the highest power X is raised to (X^2 gives you 2) then find the number of other roots useing decarts rule and subtract from total :) good luck

[harriscrl3]

Thank you so much for this you've been a great help for my PreCalc class. This is so much clearer than my Professor explained.

[minhphamdude]

thank you very much

[iheartdance21]

thank you for this! its really going to help me out on that quiz i have next week, my teacher doesnt really "teach" if you know what i mean so im stuck trying to figure it out with my textbook. but this helps alot!

[greatbambeaner]

thx for the video! i was confused about this for like a fricken hour...

[iainfs]

Does the rule tell you anything about roots at x=0?

[iainfs]

Disregard, I realised that you can just factor the x out :-(

[konopong]

Helpful presentation. Thank you!

[Anarcy06]

Could you explain how a complex root is involved?