find a polynomial function that has these zeros

Question

5 and 3-2i

Answer 1

If its coefficients are real, and one of the zeros is complex, then the complex conjugate must also be a zero.

 

f(x) = A(x - 5)[x - (3 - 2i)][x - (3 + 2i)]

 

with A real, and  A ≠ 0.

 

You can expand this if you wish.