Question

How could you use Descartes' rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial?

Your response must include:

A summary of Descartes' rule and the Fundamental Theorem of Algebra. This must be in your own words.
Two examples of the process
Provide two polynomials and predict the number of complex roots for each.
You must explain how you found the number of complex roots for each.

Answer 1

What have you done so far?

Answer 2

well i dont understand descartes rule and the fundamental theorem of algebra. ive looked at videos, definitions, asked people, and i can rememeber what they are i just dont know how to use them

Answer 3

Read more about them until you understand.
Here's another:
http://www.purplemath.com/modules/drofsign.htm

If you need comments, you will need to write a draft and post it here.
We are not allowed to write it for you, but we will be glad to help you make corrections and improvements.

Answer 4

yea all i was asking for for that part of it was just like an example and how to get to the answer by using those methods. it seems easier when i can follow with an example. and ill still make up my own and post them here.

Answer 5

Right on!

Answer 6

ok i got the definitions and understand them more but how do i make my own examples?

Answer 7

@texaschic101

Answer 8

can someone help pls? :(

Answer 9

To make an example, you can decide on the roots, and then build up the polynomial.
For example, you decide that the roots are S={3, -4, -3+i, -3-i}
Then the function would be:
f(x)=(x-3)(x+4)(x+3+i)(x+3-i) or
f(x)=x^4+7x^3+4x^2-62x-120

Now use the fundamental theorem of algebra and descartes rule as you learned them to predict the number of real and complex roots.