find a fourth degree polynomial that has zeros: 1,-3,2i

Answer 1

(x-1)(x+3)(3x-2i)(x+2i) imaginary roots come in conjugate pairs

= (x^2 +2x -3)(x^2 +4)

= x^4 +2x^3 +x^2+8x -12

or any multiple of above such as double

2x^4 +4x^3 +2x^2 +16x -24