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 complex root.

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

f (x) has three complex roots.

f (x) has three real roots.

Question

Samara Wall

Mathematics

19 August, 02:15

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 complex root.

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

f (x) has three complex roots.

f (x) has three real roots.

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Answers (1)

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Nakita · Answer 1

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

The statement that describes the number and nature of all roots for this function is:

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

Two complex roots because whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial. They come in pairs.

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