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?

Answer 1

so first off we know that the fundamental theorem of algebra tells us the umber of factors equals the number of possible roots

Answer 2

so we could predict that a polynomial of degree 5 has 5 roots

Answer 3

and Descartes rule is the change of signs rule do you remember what it tells us about the change of signs