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

Question

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

Answer 1

Since 4 + i is a root 4 - i must also be a root.

P(x) = a(x + 5)(x - 4 + i)(x - 4 - i)

P(x) = a(x + 5)(x^2 - 8x + 17)

P(x) = a(x^3 - 3x^2 - 23x + 85)