Answer:
One other zero of f(x) is (3+6i)
Step-by-step 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
[tex]f(x)=x^{4}-6x^{3}+46x^{2}-6x+45[/tex]
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)
