Question

writing polynomial functions from complex roots
if a polynomial function ( f(x) ) has roots ( -8 ), ( 1 ), and ( 6i ), what must also be a root of ( f(x) )?
options: ( -6i ), ( 6 - i ), ( 6 ), ( -6 )

Explanation:

Step1: Recall Complex Conjugate Root Theorem

For polynomials with real coefficients, if \(a+bi\) is a root, its conjugate \(a-bi\) is also a root.

Step2: Identify given complex root

The given complex root is \(6i = 0+6i\).

Step3: Find its complex conjugate

The conjugate of \(0+6i\) is \(0-6i=-6i\).

Answer:

-6i