Question

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

The degree is 4 and zeros are$1,2,2+i$

Short answer

The remaining zero of the polynomial is$2-i$.

Step-by-step solution

Step 1. Given Information 

The polynomial has degree 4 and three zeros are $1,2,2+i$

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 localid="1646230229883" $a-ib$as another zero.

Step 3. Explanation

Since f has coefficients that are real numbers, complex zeros appear as conjugate pairs. It follows that $2-i$, the conjugate of $2+i$, is the remaining zero.