Form a polynomial

Question

Form a polynomial f(x) with real coefficients having the given degree and zeros.

Degree:4

Zeros: -3+3i , 2 multiplicity 2

Anewer is in form: f(x) =a( )

Answer 1

x=-3+3i

x+3 = 3i

(x+3)^2 =-9

x^2 +6x +9 =-9

x^2 +6x + 18 =0

(x-2)^2 =0

(x-4x+4) =0

(x^2-4x+4)(x^2+6x+18) = 0

x^4 + 2x^3 -20x +72 is the 4th degree polynomial with the given zeroes