if -3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?\n-3…

if -3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?\n-3 - i\n-3i\n3 - i\n3i

if -3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?\n-3 - i\n-3i\n3 - i\n3i

Answer

Answer:

A. $- 3 - i$

Explanation:

Step1: Recall conjugate root theorem

For a polynomial function $f(x)$ with real - valued coefficients, if $a + bi$ is a root, then its complex conjugate $a - bi$ is also a root.

Step2: Identify the complex conjugate

Given the root $-3 + i$, its complex conjugate is $-3 - i$. So if $-3 + i$ is a root of a polynomial function $f(x)$ with real coefficients, then $-3 - i$ must also be a root.