Two roots of a third degree polynomial function f (x) are - 4 and 4. Which statement describes the number and nature of all roots for this function?

f (x) has three complex roots.

f (x) has three real roots.

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

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

Question

Mathematics

Stephen Buck

3 February, 04:18

Two roots of a third degree polynomial function f (x) are - 4 and 4. Which statement describes the number and nature of all roots for this function?

f (x) has three complex roots.

f (x) has three real roots.

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

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

+5

Answers (1)

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Seth · Answer 1

The Fundamental Theorem of Algebra: A polynomial of degree n with real coefficients can have at most n distinct real roots.

Roots are the solution to the polynomial. The roots may be real or complex (imaginary), and they might not be distinct. If the coefficients of polynomial are all real, the complex zeros occur in a conjugate pair. This means that the third degree polynomial may have three real roots or one real root and a pair of conjugate complex roots.

Since two roots of a third degree polynomial function f (x) are real numbers - 4 and 4, then the third root is also real.

Answer: correct choice is B.