Question

The graph of a polynomial function of degree 5 has three x-intercepts, all with multiplicity 1. Describe the nature and number of all its zeros.
A) The function has 5 real zeros.
B) The function has 3 real zeros.
C) The function has 3 real and 2 imaginary zeros.
D) The function has 2 real and 3 imaginary zeros.

Answer 1

the answer is C because the function has three x-intercepts and that means that there are three real roots. Because of the fundamental theorem of algebra, there must be a total of five roots, so the remaining two must be imaginary.