How do I find a polynomial function of lowest degree with ra

How do I find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros: 4i, 5

To cancel inner terms we have to take (-sqrt5)

the polynomial will be

=(x-sqrt(5))(x+sqrt(5))(x-4i)(x+4i)

as (a-b)(a+b) =a^2 -b^2

=(x^2 -5)(x^2 +4) as i^2 =-1

=x^4 +4x^2 -5x^2 -20

=x^4 - x^2 -20

Thank you