Use the given zero to find remaining zeros of the function

Question

f(x) = x^3 -4x^2 +4x -16 ; zero:2i

Answer 1

Step 1:

The polynomial function is .

The root of the function is

From the conjugate pair theorem, complex zeros occur in conjugate pairs.

Thus must also be a root of the polynomial.

.

is a one of the root of the function .

Thus, .

The roots of the function are

Solution :

The set of the roots of is: .