Question

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

Answer 1

Answer:

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

Step-by-step 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.