Question

If the polynomial graphed below has a degree of 5, how many imaginary zeros must it have? Why?

a) 0, because polynomials with odd degrees do not have imaginary zeros.
b) 1, because every polynomial has at least one imaginary zero.
c) 5, because the degree of the polynomial determines the number of imaginary zeros.
d) 4, because the number of imaginary zeros is always one less than the degree.

Answer 1

The correct answer is a) 0, because polynomials with odd degrees do not have imaginary zeros.

Step-by-step explanation:

The correct answer is a) 0, because polynomials with odd degrees do not have imaginary zeros.

A polynomial function with an odd degree will have at least one real zero. This is because as the graph of the polynomial approaches negative infinity on one side, and positive infinity on the other, it must cross the x-axis at least once. Since imaginary zeros represent solutions that are not real numbers, a polynomial with an odd degree cannot have any imaginary zeros.