write a fourth degree polynomial function with real coefficients that has the zeros of 4 (with multiplicity of 2) and 2-3(i)

Answer 1

A polynomial of degree 2 with zero at 4 is simply (x-4)^2.

A polynomial of degree 2 with zeros (2-3i) and (2+3i) is x^2-4x+13.

Hence, the desired polynomial of degree 4 is given by p(x)=(x-4)^2(x^2-4x+13).