find a polynomial function with real coefficients that has the given zeros

Question

4,-2i

find a polynomial function with real coefficients that has the given zeros

Answer 1

x = 4

x-4 = 0

x-4 is one factor

x = -2i

x^2 = -4

x^2 +4 =0

x^2+4 is another factor

multiply the factors

y = (x-4)(x^2+4)

f(x) = x^3 -4x^2+4x -16 is the polynomial fuction with the given zeros