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.

Question

Cristal Carrillo

Mathematics

19 December, 19:02

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.

+5

Answers (1)

Know the Answer?

Madilynn Ball · Answer 1

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