Degree 3 polynomial with real coefficients and zeros 4 and 5i

Question

Write a polynomial f (x) that meets the given conditions.

Answer 1

The complex conjugate of a complex zero must also be a zero, so the 3 zeros are

4

5i

-5i

f(x) = A(x - 4)(x - 5i)(x + 5i) = A(x - 4)(x² + 25),

where A is real and A ≠ 0. You can expand to standard form if you wish.