Question

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

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

Short answer

The remaining zero of the polynomial is$-i$

Step-by-step solution

Step 1. Given Information

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

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$i$ is the remaining zero.