# How do you find the number of roots for #f(x) = 4x^5 – 2x – 15# using the fundamental theorem of algebra?

##### 1 Answer

#### Explanation:

The Fundamental Theorem of Algebra tells us that any non-constant polynomial equation with Complex (possibly Real) coefficients has at least one Complex (possibly Real) zero.

A simple corollary of this is that a polynomial of degree

To show the corollary: Suppose

So in the case of

**Bonus**

What else can we find out about these zeros?

First note that the sequence of coefficients of

In fact, we can see that

If we reverse the signs of the coefficients of the terms of odd degree, then all are negative. So

Since the coefficients of

So we must have two pairs of Complex conjugate zeros and one positive Real zero.