Question

Three roots of a fifth degree polynomial function f(x) are -2, 2, and 4 + i. Which statement describes the number and

nature of all roots for this function?

A) f(x) has two real roots and one imaginary root.


B) f(x) has three real roots.


C) f(x) has five real roots.


D) f(x) has three real roots and two imaginary roots.

Answer 1

D.

Explanation:

Its a fifth degree function so it will have 5 roots.

One of the 3 roots is complex ( imaginary):- 4 + i so there must be another root value 4 - i because these roots always occur as conjugate pairs.

The fifth root must be real because you cant have just one imaginary root.