How to find a polynomial when only given its zeros

Question

find a 5th degree polynomial function with real coefficients that has zeros: -2,3, and 2+i

Answer 1

For the coefficients to be real, the complex conjugate of a complex zero must also be a zero. Hence, you have 4 zeros:

-2

3

2 + i

2 - i

To get a 5th degree polynomial, you need to provide another real zero, or state that one of the zeros has a multiplicity of 2. Is there another zero that was not included in the problem statement?