if 9i is a root of the polynomial function f(x), which of the following must also be a root of…

if 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?\n-9i\n-\\frac{1}{9}i\n\\frac{1}{9}i\n9 - i

if 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?\n-9i\n-\\frac{1}{9}i\n\\frac{1}{9}i\n9 - i

Answer

Answer:

A. $-9i$

Explanation:

Step1: Recall conjugate root theorem

If a polynomial function $f(x)$ has real - valued coefficients and $a + bi$ is a root of $f(x)$, then its complex conjugate $a - bi$ is also a root of $f(x)$. The given root is $9i=0 + 9i$. Here $a = 0$ and $b = 9$.

Step2: Find the conjugate

The complex conjugate of $9i$ is $0-9i=-9i$. So if $9i$ is a root of a polynomial with real - valued coefficients, then $-9i$ must also be a root.