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?
Of(x) has two real roots and one imaginary root.
f(x) has three real roots.
f(x) has five real roots.
Of(x) has three real roots and two imaginary roots.

Answer 1

Answer: ITS D (f(x) has three real roots and two imaginary roots)

Answer 2

We know that imaginary roots always come in pairs, so we already know 4 solutions

-2, 2, 4 + i and a pair of 4 + i

Since imaginary roots always come in pairs we wont have more than 2 imaginary roots, since its a fifth degree root and we can only have 5 roots

So for sure, we will have 3 real roots and 2 imaginary roots

Last option, f(x) has three real roots and two imaginary roots