Question

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

The degree is 5 and zeros are$0,1,2,i$

Short answer

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

Step-by-step solution

Step 1. Given Information

The polynomial has degree 5 and four zeros are$0,1,2,i$.

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 $i$ is the remaining zero.