Question

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its

zeros.
- 2i, 4

Answer 1

x³ - 4x² + 4x - 16

Explanation:

Since the coefficients are real, the complex zeros come in complex conjugate pairs. If -2i is a zero, then 2i must also be a zero.

The zeros are -2i, 2i, 4

(x - (2i))(x - (-2i))(x - 4) =

= (x - 2i)(x + 2i)(x - 4)

= (x² + 4)(x - 4)

= x³ - 4x² + 4x - 16