Question

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

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

Short answer

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

Step-by-step solution

Step 1. Given Information

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

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

$i$Since the function has coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that $-i$, the conjugate of $i$, and $-2i$, the conjugate of $2i$, are the two remaining zeros.