16
QuizMultiple Choice

The Fundamental Theorem of Algebra

Question 16 • 270311 - UCLA - Algebra 2 (semester 1)

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?

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

Explanation

A third-degree polynomial has three roots when counted with multiplicity. Since its coefficients are real and two roots are the real numbers −4 and 4, the remaining root must also be real: any nonreal roots of a real polynomial occur in conjugate pairs, which cannot fit as just one remaining root. Therefore, f(x) has three real roots.

AI-written and checked against the verified answer.

Previous
Next