fourth degree polynomial function with real coefficients; zeros : -2, 0, 3 + i

Question

fourth degree polynomial function with real coefficients; zeros : -2, 0, 3 + i

Answer 1

The complex conjugate of a complex zero must also be a zero, so you have 4 zeros:

-2

0

3 + i

3 - i

The polynomial is

f(x) = Ax(x + 2) [x - (3 + i)] [x - (3 -i)],

with A real and A ≠ 0. You can expand to standard form if you wish. The coefficients will all come out real.