Find the polynomial function with real coefficients that has the given zeros

Question

4, -2i

Answer 1

4, -2i are zeros. imaginary zeros come in conjugate pairs, so a 3rd zero is 2i

change the sign of each zero, stick an x in front of it, then multiply the factors together to get:

P(x) = (x-4)(x+2i)(x-2i) = (x-4)(x^2+4)

P(x) = x^3 -4x^2 +4x -16