Find a polynomial

Question

Find a polynomial P(x) with real coefficients having a degree 4, leading coefficient 2, and zeros 3-i and 3i

Answer 1

The complex conjugates of complex zeros must also be zeros, so your 4 zeros are

3 - i

3 + i

3i

-3i

P(x) = 2 [x - (3 - i)] [x - (3 + i)] (x - 3i) (x + 3i)

Expand to standard form if you wish. All the coefficients will come out real.