Question

Using the given zero, find one other zero of f(x). 3 - 6i is a zero of f(x).= x4 - 6x3 + 46x2 - 6x + 45.

Answer 1

All the possible roots are:

x= i, -i, 3+6i, 3-6i.

Answer 2

One other zero of f(x) is (3+6i)

Explanation:

we know that

The Conjugate Zeros Theorem states that if a complex number a + bi is a zero of a polynomial with real coefficients then the complex conjugate of that number, which is a - bi, is also a zero of the polynomial

In this problem we have

`f(x)=x^(4)-6x^(3)+46x^(2)-6x+45`

Is a polynomial with real coefficients

so

If (3-6i) is a zero of f(x)

then

The complex conjugate of that number, is also a zero of the polynomial

The complex conjugate is (3+6i)

therefore

One other zero of f(x) is (3+6i)