Question

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

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

Short answer

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

Step-by-step solution

Step 1. Given Information

The polynomial has degree 6 and three zeros are$i,3-2i,-2+i$.

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 $-i$, the conjugate of $i$, $3+2i$, the conjugate of $3-2i$, and $-2-i$, the conjugate of $-2+i$ are the remaining three zeros.