solve the equation

Question

find a polynomial with deg f= 3 that has zeros 1, and 2i.

(hint: use the Conjugate Pairs Theorem to find the third zero.) 

Answer 1

(x-1)(x^2 +4)

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

x = 2i and -2i

corresponding factors are x-2i and x+2i

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