Question

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

The degree is 4 and zeros are$2-i,-i$

Short answer

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

Step-by-step solution

Step 1. Given Information

The polynomial has degree 4 and two zeros are$-i$and$2-i$.

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