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?

For a polynomial with real coefficients, any nonreal complex root must occur with its conjugate. So if –5 + 2i is a root, –5 – 2i is also a root. These are two nonreal roots, and a third-degree polynomial has one root left; because nonreal roots come in conjugate pairs, that remaining root must be real. Thus the function has two imaginary (nonreal complex) roots and one real root: choice B.

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