Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all roots for this function?
* f(x) has three imaginary roots.
* f(x) has three real roots.
* f(x) has two real roots and two imaginary roots.
* f(x) has three real roots and one imaginary root.

f(x) has three real roots.

Step-by-step explanation:

f(x) has three real roots.

A third degree polynomial function with real coefficients has exactly 3 roots.

Furthermore, all complex roots come in pairs, either there is none, or there are exactly two conjugates, which are in the form e1+i(e2) and e1-i(e2) where e1 and e2 are polynomial expressions.

This also means that a third degree polynomial with real coefficients has at least one real root, or three.

Since we are given two real roots for the given polynomial, the third root cannot be complex alone, so the only possibility is that there are three real roots.

it has three real roots

Step-by-step explanation: B