Question

A polynomial function of degree 4 with real coefficients could have -3, 2 + i, 2 - i, and -3 + 5i as its zeros. True or False

Answer 1

(x+3)(x-2-i)(x-2+i)(x+3-5i)=0
(x+3)(x2 -4x +4 +1)(x+3 - 5i)=0
(x+3)(x2 -4x +5)(x+3-5i) =0

so the ans is FALSE because there is nothing in the polynomial function to make (x+3 - 5i) real.

Answer 2

@Koel Thank you