Find a third-degree polynomial equation with rational coefficients that has roots 5 and 4i

Question

Find a third-degree polynomial equation with rational coefficients that has roots 5 and 4i

Answer 1

The complex conjugate of a complex zero must also be a zero, so you will have 3 zeros:

5

4i

-4i

f(x) = A(x - 5)(x - 4i)(x + 4i) = A(x - 5)(x² + 16),

where A is a real, nonzero rational number.