if (f(x)) is a third - degree polynomial function, how many distinct imaginary roots are possible?\n0 or…

if (f(x)) is a third - degree polynomial function, how many distinct imaginary roots are possible?\n0 or 2\n0, 1, 2, or 3\n1 or 2\n1, 2, or 3

if (f(x)) is a third - degree polynomial function, how many distinct imaginary roots are possible?\n0 or 2\n0, 1, 2, or 3\n1 or 2\n1, 2, or 3

Answer

Answer:

A. 0 or 2

Explanation:

Step1: Recall conjugate root theorem

Complex (imaginary) roots of a polynomial with real - coefficients occur in conjugate pairs.

Step2: Consider degree of polynomial

A third - degree polynomial has 3 roots (counting multiplicities) according to the fundamental theorem of algebra.

Step3: Analyze number of imaginary roots

Since imaginary roots come in pairs, the number of distinct imaginary roots of a third - degree polynomial can be 0 (when all roots are real) or 2 (when there is one real root and a pair of conjugate imaginary roots).