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How to use Descartes rule of signs to determine the number of positive and negative zeros

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👉 Learn about Descartes' Rule of Signs. Descartes' rule of the sign is used to determine the number of positive and negative real zeros of a polynomial function. Knowing the number of positive and negative real zeros enables also to also know the number of complex zeros of a complex number.
Descartes' rule of signs states that the number of positive real zeroes in a polynomial function f(x) is the same or less than by an even number as the number of changes in the sign of the coefficients of the terms of the polynomial function. The number of negative real zeroes of the f(x) is the same as the number of changes in sign of the coefficients of the terms of f(-x) or less than this by an even number.
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Опубликовано:

23 авг 2024

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Комментарии : 156

@calvin3448 5 лет назад

Dude I think you need to buy more expos. You don’t look like you have enough.

@ermiles6472 5 лет назад

it's really hard to have too many expo pens

@carlosdominguez3133 4 года назад

No such thing as too many

@Yoh_Mama 3 года назад

You can never have plenty you can only have enough

@kaylad.6427 7 лет назад

YOU ARE SAVING ME IN MY ALGEBRA TWO CLASS YOU ARE A HERO BECAUSE MY CURRENT ALGEBRA TEACHER IS JUST A PIECE OF TRASH THANK U NOW I HAVE A HOPE OF PASSING THIS CLASS

@brianmclogan 7 лет назад

sorry to hear, happy to be able to help you out

@smrtturtle5629 3 года назад

no cap

@spider6060 Год назад

hate my alergebra 2 teacher shes the type to try her hardest to even when you get the answer right take as many points off in places where it doesnt even matter

@giovi7461 Год назад

so real

@rohtosftw123 5 лет назад

I bet this teacher has some killer ink on his arms. he's always wearing long sleeves.

@geovanygrant5298 3 месяца назад

What a thought process

@geovanygrant5298 3 месяца назад

What a thought process

@dariust.barrett5575 Год назад

I’m a senior in college majoring in computer science I just want to say Thankyou for being one of the best math teachers I’ve had in the years I’ve been watching your videos to understand things that were confusing because it wasn’t taught adequately

@ContortyEva 5 месяцев назад

Damn same here - except sophomore in college 🥲

@Wendykenson 7 лет назад

0:37 yeah AMBER....

@brianmclogan 7 лет назад

: )

@brianmclogan 11 лет назад

I understand your confusion. The rule states that the number of zeros is the number of sign changes or minus an even number. For instance lets just focus on positive zeros even though this is also the case for negative zeros. Lets say for your function you have 1 sign change. Therefore there is one possible positive zero. You cannot subtract an even number because then you would have a negative amount of positive zeros.

@Lalooooo Год назад

that cleared my confusion thank you

@unaccademyuserprt 10 месяцев назад

the maximum number of +ve roots, including the imaginary roots, are at most equal [ not exactly equal to ] the numvber of sign changes in f(x) and the chances of +ve roots decreases by 2 because imaginary roots occurs in pairs

@amberreyna8042 3 года назад

LMAO my name is Amber and I looked down at my page when he said “Amber” and I got so scared for a second 😭😂

@uravityuraraka1327 4 года назад

You sir have made my life so much easier with online school and the corona quarantine. When students cant go to teachers anymore its good to have a back up plan and you have provided it :)

@brianmclogan 11 лет назад

next example. Lets say you have two sign changes in your equation. Then you will have two or zero possible zeros because 2 minus 2 is zero. Next example lets say you have five sign changes in your equation. They you will have 5 possible zeros or 3 or 1 because those are the other values you get when you subtract even numbers from 5. Hope this helps. Remember the rule does not state the number of zeros is only the sign changes. Its the number of sign changes OR minus an even number

@aj8gajardo771 4 года назад

ohhhhh...Thank you.

@vamsik7705 2 года назад

Thank You So Much Sir🙏...

@Quixler 10 месяцев назад

Thank you man! I was so confused about the subtraction part to find the other number of real zeros.

@levismith4515 4 года назад

Amber, come on!

@aabbcc7532 4 года назад

Dude I'm back in school for engineering after 7 years of working and 5 years of industry specific schooling in the electrical industry. You are a lifesaver I get so much more done going through your videos than my textbook. Rock on

@claytonmoore1029 2 года назад

It is so refreshing to have a confident and engaging teacher give explanations like these. I have a wonderful calculus teacher but we spend more class time on notes then on application and your videos have been a genuine help to understanding the notes I've written down

@galjoferatovic3660 5 лет назад

2:33 my right ear appreciates the rest of the lecture

@raahisaoji2224 3 года назад

Same

@omari2292 2 года назад

You've made this semester a lot easier for me (still rough) but you've come through for me so many times, thank you

@rookiemvp2008 5 лет назад

If my college professors were this good at teaching math classes, It'd make the cost of tuition worth it!

@tahakhalafi5460 6 месяцев назад

This RU-vid channel and all your RU-vid videos are goated. You are probably the greatest RU-vidr of all time. I hope you make money from this

@ThaoNguyen-yb6xq Год назад

I'm self-studying precal right now and I cannot get by without you!!! I would read the textbook and if something is confusing voila there is a Mr. McLogan video to help me!

@brianmclogan Год назад

💪💪💪

@theawesomeotaku4590 4 года назад

Clear and concise, thanks! You just helped make some sense of what's going on in my math class.

@oliviasierra9472 3 года назад

Thanks for being helpful, unlike my FST teacher 🙃

@peytonhampton514 3 года назад

Lifesaver! My teacher decided to say sorry I didn't teach this to you but it's going to be on your final tomorrow so I hope you know it. God bless you for the help!

@peytonhampton514 3 года назад

Update: I got an A!

@KevinHernandez-hy1qb 10 месяцев назад

@@peytonhampton514 w

@truongdang8130 4 года назад

this was so much easier than reading the damn books lol, thank you

@MountShine 3 года назад

online school is stupid

@mohamedalsaadany106 6 лет назад

thank you for your effort you are amazing, you helped me a lot

@brianmclogan 6 лет назад

happy to be able to help Mohamed!

@MountShine 3 года назад

reliable as always, much better than any of the textbooks or teachers I had online

@WarrenMurphy-cj7in 6 месяцев назад

Great video... I was so lost before I found this. Thank you!

@rumbi16 4 года назад

Brian you are a great tutor. hats off

@lucid6607 Год назад

This guys videos always help so much when I did not understand class

@abdulshrif215 3 года назад

Thanks a lot man this really helped me with my online class

@brianmclogan 11 лет назад

correct!

@rivieraaguilera732 4 года назад

You explained it perfectly! The textbook always makes it confusing

@brianmclogan 4 года назад

Happy to help

@NarutoUzumaki-nk7kp 3 года назад

@@brianmclogan you are great replying to a comment on a 7 year old video👍👍👍👍👍

@brianmclogan 11 лет назад

I cannot where I went wrong, can you explain where we differ?

@AJ-et3vf 11 месяцев назад

What if there are zero coefficients? Like positive number then zero, or negative number then zero. Is that a sign change?

@brianmclogan 11 лет назад

awesome!

@mobinsk229 Год назад

From INDIA... Awesome class

@5gallonsofwater495 11 месяцев назад

currently a freshman in college majoring in electrical engineering, and woo is it sweet to brush up on your algebra for them calculus questions

@Mphuthiln101 2 года назад

So happy you reached 1M subscribers.

@brianmclogan 2 года назад

Thanks!!

@marguuh9443 2 года назад

THANK YOU SO MUCH FOR HELPING ME I WILL NEVER FORGET YOU

@donmoody577 7 лет назад

I see you, ending your video at 4:20

@brianmclogan 7 лет назад

absolutely!

@generalgrievous3731 4 года назад

@@brianmclogan Only a Sith deals in absolutes

@Tony-tk4ht 3 года назад

Thank you for your service

@kulpreetkaur323 6 лет назад

thank you very much sir

@brianmclogan 6 лет назад

you are very welcome Kulpreekaur!

@IamCurrentlyAscending 2 года назад

I would just like to take a moment to appreciate the amount of dry erase markers available. My teachers are either hunting for one, or trying to find one that writes. This looks like a sure situation.

@vamsik7705 2 года назад

Thank You So Much Sir for clear Explanation 🙏

@bushraayman2587 3 месяца назад

Thank you!

@realbruh850 10 месяцев назад

thanks im studying in high school rn was confused abt this

@Angelboy_04 2 года назад

Lifesaver! Thank you 🙏

@seungbumlee2647 9 месяцев назад

Saved my life

@brianmclogan 11 лет назад

sorry

@acefxrce3235 2 года назад

The dude that laughed when he said imaginary really wants some extra credit🤣

@yaseengaffoor 3 года назад

My right ear thanks you 2:32

@jibeeeee 3 года назад

Thanks for the lesson lods.

@westmantooth210 11 лет назад

I get it. Thanks Brian!

@shyamleela6252 2 года назад

thank you so much

@alexalopez4904 Год назад

So helpful!!!

@leadinglife534 3 года назад

Love your vids

@ariannaadame2365 2 года назад

How does the (-x)^2 change to positive?

@brianmclogan 2 года назад

-x*-x = positive

@allen8478 4 года назад

Ends at 4:20

@EllieandDreams 4 года назад

thanks for saving my butt in my Algebra II class 😭😂

@amberhall1119 Год назад

At 0:38 my stomach dropped into my ass. Lol "What this tells us is the number, AMBER". It's been a while since a teacher has said my name like that.

@ankitasarkar3569 6 лет назад

Thank you sir.. But what happens if there is no sign changes ??

@brianmclogan 6 лет назад

for f(x) then there will be no real positive zeros, if for f(-x) then there will be no real negative zeros

@ankitasarkar3569 6 лет назад

Brian McLogan thank you so much sir

@brianmclogan 6 лет назад

cheers! 👍

@almiragraceb.dagcuta486 6 лет назад

@@brianmclogan sir what would be its positive real roots if the variation of signs is 6?

@zyrxom 2 года назад

do i always use the smallest positive number?

@kionna1984 11 лет назад

Please let me know if I am right, after watching your video a few times I got # of real postive roots: 2,0 # of negitive roots is exactly 1 ????

@WILL_DYNASTY 2 года назад

Appreciate you!

@l1fer233 5 месяцев назад

In 4 minutes you explained something that took my teacher 90 minutes and she still didn’t make it make sense 😂

@sorianics Год назад

thankyoiu

@hajerafarooq9478 2 года назад

What are irrational and rational roots? and also what are complex numbers

@tree479 3 года назад

How tf do you get the chart, I’m so stuck on that part

@abigailalidon3842 3 года назад

so this video is 7 years ago..but still helps me a lot

@Carmen-sp4vf 5 месяцев назад

I'm lost from the beginning. Where did he get the 2 for the even number? The smallest even number in the equation is 4.

@ashleylacasse3769 4 года назад

great video

@yahshuaurielojastro 5 лет назад

TYSM

@toxicmaniax5719 2 года назад

What about non real complex zero?

@woobinkwon2259 4 года назад

What school you teach now?

@huntermiller7846 2 года назад

Thank you Brian you are the goat

@brianmclogan 2 года назад

Happy to help!!

@MountShine 3 года назад

you are my teacher since algebra1 to pre-cal XD

@westmantooth210 11 лет назад

Yeah your right. I forgot the minus sign in front of the coefficient. I still puzzle over what you mean at 2:14 - 2:30.

@micahpaik5445 2 года назад

I love you.

@Infinitepower99 Год назад

Sir , x² +10x +39 =0 , from Dcartes rule 2 roots AND from Discriminant B² - 4AC they are imaginary HOW ?????

@brianmclogan Год назад

Descartes does not say how many it gives possible and Descartes would be 0 real rational which the discriminant confirms

@JayuuUshir 5 месяцев назад

Who is watching in 2024

@mrAZcardinal 3 года назад

"What this tells us, is the number, AMBER..."

@bokelos3497 4 года назад

f(x)=x^3-7x^2+6x+20 HELP? not work on Descartes rule of signs

@udeleted8075 3 года назад

I got an exam tomorrow and this just saved me. Thanks.

@crowncloud3337 4 года назад

Did you comb your hair senpai

@boldcardo9820 3 года назад

2:28 i thought my earphones broke

@minilamma4879 Год назад

I bet 10 bucks that you got those expo pens from receiving them for extra credits

@Ninja-tp8xs 3 года назад

Bro, this is same problem I’m working on.

@Mathguy534 2 года назад

Ive never seen anything like it in my life

@brianmclogan 2 года назад

Like what?

@user-xz6cd7ql4e 3 года назад

What about the imaginary root?

@chanakyasinha8046 4 года назад

Didn't got the intuitive understanding :(

@milesninasontousidadgaso7766 3 года назад

but how do you find imaginary zeros?

@milesninasontousidadgaso7766 3 года назад

the number of imaginary zeros!*

@milesninasontousidadgaso7766 3 года назад

@snowflake8191 3 года назад

king

@srikarbala246 4 года назад

Sub war between Mario's and Brian McLogan's

@kionna1984 11 лет назад

Use Descartes’ Rule of Signs to state the number of possible positive real zeros and the number of negative real zeros of P(x) = 4x^4-6x^3-x^2-x+11 Where do I start?

@KingOfSweden007 4 года назад

🐐

@scaredsamurai6974 4 года назад

Pay attention *Amber.*

@liamwalsh9281 4 года назад

how old are you hi

@kendao8216 4 года назад

Am I the only one that heard someone blow a loud ass sneaky fart at 1:27?

@jesseplayz8889 5 лет назад

Youre right school is boring AF

@westmantooth210 11 лет назад

There shouldn't be any negative zeros. -4 X -x^2 = 4x^2

@mooseyman5000 5 лет назад

Yeah wouldnt it be? -4(-x)^2 =4x^2? In taking f(-x) you left that portion un changed. Although it would make the overall f(-x) = -3x^3 + 4x^2 + 17x + 6 and still only having one sign change

@aidenaune7008 3 года назад

@@mooseyman5000 -4(-x^2)=-4(-x*-x)=-4*-(x*x)=4(x*x)=4x^2

@mooseyman5000 3 года назад

@@aidenaune7008 yes in my reply that is my point, which is why I’m saying the sign change should be happening between the -3x^3+4x^2 and not between -4x^2+17x like shown in the video at 3:47 for the f(-x)