Like rational zero theorems tell us the possible zeros of a polynomial after dividing constant factors over the leading coefficient factors, and upper and lower bonds help us lower that search and cut out the greater numbers ( if it's in upper bond) or lesser (if its lower bond) than that number, so does the Descartes' Rule of Sign also says that there are x amount of possible zeros in a polynomial or it says that the amount of real negative or real positive number you find in Descartes' rule of the sign by checking the change of signs means that possible amount of real positive or negative number can only be that certain amount? For example, I find 10 numbers in the rational zero theorem and then I use Descartes' rule of sign to find out that I can only have 4, 2, 0 positive real numbers and 2 or 0 real negative numbers. So does that mean including the 10 numbers I found in the rational zero theorem (which means 20 numbers because 10 negative and 10 positives) I will find only 4, 2, or 0 positive numbers in any positive value between 1 and 10 in the rational zero theorem and 2 or 0 negative numbers in 1 to 10 numbers in the rational zero theorem? Like for example, I can have 4 positive real numbers so I can pick 6, 7, 8, 9, or negative then -3, -8. or it says exactly 4, 2, 0 + real and 2, 0 - real inside the rational zero theorem or does Descarte's rule of sign give possible zeros like the rational zero theorem but narrow the possibility down? What category is this video in? I found this on Yt because I needed help and a better explanation than my textbook and I can't see it in the category.
openstax.org/books/college-algebra-2e/pages/5-introduction-to-polynomial-and-rational-functions Work through 5.1, 5.2, 5.3, 5.4, and 5.5 in order. That will answer all of your questions on this topic. Make sure to do practice, which is included at the end of each section. Good luck!
@GravitySix-G6 There is no such thing as the best book. The book you are using is just fine and is probably 99% similar to any other Algebra book. The main thing is to go in order and work all the practice in the book. If you do that, you will get really good at math!
Hello sorry for the lengthy question. I was preparing for my exams and I came across a question where it required me to count the number of real roots for the expression: x^3 - 300x - 3000 = 0. I used the method described in the video and I came up with 1 positive real root, and 2 negative real roots. The answer was 1 real root only. I do realize that it is possible for there to be either 2 negative real roots or 0 negative real roots, but i'd like to ask how do we determine when to subtract? in this case it is not as obvious to me because 1 positive and 2 negative real roots add up to exactly 3 number of real roots
For f(x), you get 1 sign change so 1 positive root For f(-x), you get 2 sign changes so 2 negative roots or 0 negative roots When you say when do we determine when to subtract? You set up a table with the possibilities as done in the video. It tells you what is possible. Here it is possible to have 2 negative roots or 0 roots and you see you get 0 negative roots.
If you did not get it, it is because you can not have a negative number of negative solutions. Therefore by Descartes rule of signs we must have 1 negative solution since 1-2= -1 and again we cannot have a negative number or solutions.
THANK YOU SO MUCH, I AM SO CONFUSED ON WHAT TO DO AND THIS HELPED ME
Glad it helped!
Thankyou So much you helped me a lot.It was easy after u explained it.
You are welcome! 😎
Like rational zero theorems tell us the possible zeros of a polynomial after dividing constant factors over the leading coefficient factors, and upper and lower bonds help us lower that search and cut out the greater numbers ( if it's in upper bond) or lesser (if its lower bond) than that number, so does the Descartes' Rule of Sign also says that there are x amount of possible zeros in a polynomial or it says that the amount of real negative or real positive number you find in Descartes' rule of the sign by checking the change of signs means that possible amount of real positive or negative number can only be that certain amount?
For example, I find 10 numbers in the rational zero theorem and then I use Descartes' rule of sign to find out that I can only have 4, 2, 0 positive real numbers and 2 or 0 real negative numbers. So does that mean including the 10 numbers I found in the rational zero theorem (which means 20 numbers because 10 negative and 10 positives) I will find only 4, 2, or 0 positive numbers in any positive value between 1 and 10 in the rational zero theorem and 2 or 0 negative numbers in 1 to 10 numbers in the rational zero theorem? Like for example, I can have 4 positive real numbers so I can pick 6, 7, 8, 9, or negative then -3, -8. or it says exactly 4, 2, 0 + real and 2, 0 - real inside the rational zero theorem
or does Descarte's rule of sign give possible zeros like the rational zero theorem but narrow the possibility down?
What category is this video in? I found this on Yt because I needed help and a better explanation than my textbook and I can't see it in the category.
openstax.org/books/college-algebra-2e/pages/5-introduction-to-polynomial-and-rational-functions
Work through 5.1, 5.2, 5.3, 5.4, and 5.5 in order. That will answer all of your questions on this topic. Make sure to do practice, which is included at the end of each section. Good luck!
@@Greenemath thank you! Have you heard of Miler College Algebra edition 2 book? What do you think of it?
@GravitySix-G6 I haven't heard of that book or used it. I use Lial and Sullivan for College Algebra. All of the books are mostly the same.
@@Greenemath Oh. Which book do you consider the best in your opinion?
@GravitySix-G6 There is no such thing as the best book. The book you are using is just fine and is probably 99% similar to any other Algebra book. The main thing is to go in order and work all the practice in the book. If you do that, you will get really good at math!
It was a very helpful video to learn decarts rule of sign....
glad you found it helpful.
Hello sorry for the lengthy question. I was preparing for my exams and I came across a question where it required me to count the number of real roots for the expression: x^3 - 300x - 3000 = 0. I used the method described in the video and I came up with 1 positive real root, and 2 negative real roots. The answer was 1 real root only. I do realize that it is possible for there to be either 2 negative real roots or 0 negative real roots, but i'd like to ask how do we determine when to subtract? in this case it is not as obvious to me because 1 positive and 2 negative real roots add up to exactly 3 number of real roots
For f(x), you get 1 sign change so 1 positive root
For f(-x), you get 2 sign changes so 2 negative roots or 0 negative roots
When you say when do we determine when to subtract? You set up a table with the possibilities as done in the video. It tells you what is possible. Here it is possible to have 2 negative roots or 0 roots and you see you get 0 negative roots.
Finding real zeros or roots means x intercept right? why do we call imaginary numbers also zeros?
Work your way through this article, I think it gives a very good explanation of things.
www.cuemath.com/algebra/zeros-of-a-function/
Thanks for the help. I understand it now
You're welcome!
Great video! Thank you
Glad you liked it!
What do you do when you dont have a number with no x at the end?
What's the example you are working with?
Sir in 2nd example why there is only 1 possiblity why other possiblity 0,0 ,4 doesn't exist plzz explain🥺
Did you get this yet?
If you did not get it, it is because you can not have a negative number of negative solutions. Therefore by Descartes rule of signs we must have 1 negative solution since 1-2= -1 and again we cannot have a negative number or solutions.
And 0,0,4 isn't a possibility either since you have a sign change in f(x)
So in short, we just find the amount of possibilities?
Yes, that is the idea. Usually, you are using this as part of a full series of steps designed to allow you to find the zeros of a polynomial function.
Thank you sir 👍
Welcome!
Well done
Thank you for the nice comment! 😎