Question

One root of a third degree polynomial function f(x) is -5 + 2i. Which statement describes the number and nature of all

roots for this function?
f(x) has two real roots and one imaginary root.
f(x) has two imaginary roots and one real root.
f(x) has three imaginary roots.
f(x) has three real roots.

Answer 1

B!

Explanation:

just did it

Answer 2

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

Explanation:

Complex roots:

I a complex number
`a + bi` is a root of a polynomial, it's conjugate
`a - bi` is also a root.

One root of a third degree polynomial function f(x) is -5 + 2i.

This means that -5 - 2i is another root of the polynomial, and thus, 2 of the roots are complex.

Third degree, so it has three roots, which means that the third root is real(not possible to have a complex root without it's conjugate), and thus, the correct answer is:

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