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.

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.

anonymous · Answer

I read and looked up a lot on this question, but I am still having problems putting it into words

anonymous · Answer

@Hero

anonymous · Answer

You can use Descarte's Rule of Signs to find the maximum number of positive and negative real zeros to a polynomial. The Fundamental Theorem of Algebra can be use to find the maximum number of total zeros. Then subtract the number of real zeros from the total zeros to obtain the complex zeros.