PLEASE HELPPP!!!!! 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.Two examples of the process
Provide two polynomials and predict the number of complex roots for each. explain how you found the number of complex roots for each.

Question

PLEASE HELPPP!!!!! 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.Two examples of the process
Provide two polynomials and predict the number of complex roots for each. explain how you found the number of complex roots for each.

anonymous · Answer

You can use Descarte's Rule of Signs to find the maximum number of positive and negative real zeros to a polynomial. Then, you can use Fundamental Theorem of Algebra to find the maximum number of total zeros (real and complex). Then, just subtract the number of real zeros from the total zeros to obtain the complex zeros. Is this right?