Question

Find the remaining zeros of $f\left(x\right)$with real coefficients and given information.

The degree is 6 and zeros are$2,2+i,-3-i,0$

Short answer

The remaining two zeros of the polynomial are$2-i,-3+i$.

Step-by-step solution

Step 1. Given Information

he polynomial has degree 6 and four zeros are$2,2+i,-3-i,0$.

Step 2. Concept

Conjugate Pair Theorem says that if a polynomial with degree $n$with real coefficient, has one complex zero of the form $a+ib$then the polynomial should have the conjugate pair of $a+ib$that is $a-ib$ as another zero.

Step 3. Explanation

Since the function has coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that $2-i$, the conjugate of $2+i$, and $-3+i$, the conjugate of $-3-i$, are the remaining two zeros.