Question 971583: If 3i is a zero of f(x)= x^4-2x^3+6x^2-18x-27, find all the zeros and write the answer in factored form. Thanks Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! f(x)= x^4-2x^3+6x^2-18x-27
(x+3i) (x-3i) are factors, since they are conjugate.
These multiply to x^2-9i^2=x^2+9
The other factor must contain a -3, since the constant is -27
Divide that into the original polynomial, and we get x^2-2x-3= (x-3) (x+1)
The zeros are +/- 3i , 3, -1 . The latter two produce 0 in the polynomial.
The factored form is (x+3i)(x-3i)(x-3)(x+1)
