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

I'm really struggling with this one

Answer 2

This video might help you understand this rule better: http://www.youtube.com/watch?v=1utFwnmBOyU

Answer 3

it didn't help really

Answer 4

you watched it all THAT QUICKLY?

Answer 5

here is another description of the rule: http://www.purplemath.com/modules/drofsign.htm

remember the question is asking you to describe this in "your own words"

Answer 6

Decartes' Rule of sing pretty much explains the amount of all of the positive and negative real roots or the imaginary roots for each and every function.Then, you can use Fundamental Theorem of Algebra to find the most number of total zeros Then, just subtract the number of real zeros from the total zeros to get the complex zeros.

Answer 7

that is roughly correct - but I would add a little more detail to it. You haven't really explained what Descartes Rule of Signs is and how to apply it, you have instead stated what it does. It might help if you used an example to illustrate the rule.

Answer 8

ohh ok what would be a good example

Answer 9

just make up a polynomial, say a 3rd or 4th degree one.

Answer 10

the easiest

Answer 11

in the case of this rule there isn't really an "easiest" one. the rule is just as easy to apply to a polynomial of any degree.

Answer 12

i guess but it so hard for me to put everything in words:/

Answer 13

I would re-watch that video to the end - the guy does explain this rule very well.

Answer 14

?