Question

The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
A) The function has one imaginary zero.
B) The function has one real zero and two imaginary zeros.
C) The function has one real zero and one imaginary zero.
D) The function has one imaginary zero and two real zeros.

Answer 1

If a polynomial function with real coefficients has any complex roots, then the complex roots come in pairs of complex conjugates.
Your polynomial has real coefficients and is of degree 3.
It can have 0 complex roots, or it can have 2 complex roots.
It cannot have only 1 complex root.

Answer 2

The correct answer is

D) The function has one imaginary zero and two real zeros.

x = 3, 4i, -4i