Find polynomial function with real coefficients that has the given zeros

Question

1. 4, -5i
2. 4, 7 + i

Answer 1

1)

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

(x-4)(x^2 + 25) =

x^3 - 4x^2 + 25x - 100

2)

(x-4) [ (x-7)+i] [ (x-7) - i ]

(x-4) [ (x-7)^2 + 1]

(x-4) ( x^2 - 14x +50)

x^3 - 4x^2 - 14x^2 + 56x + 50x - 200

x^3 - 18x^2 + 106x - 200