Polynomials with degrees

Question

Find a polynomial f(x) of degree 3 with real coefficients and the following zeroes. 4, -2i

Answer 1

To ensure real coefficients, the complex conjugate of any complex zero must also be a zero. Therefore your 3 zeros are

4

-2i

2i

f(x) = A(x - 4)(x + 2i)(x - 2i) = A(x - 4)(x² + 4),

with A real and A ≠ 0.