Question

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

The degree is 3 and zeros are$4,3+i$

Short answer

The remaining zero of the polynomial is $3-i$.

Step-by-step solution

Step 1. Given Information

The polynomial has degree 3 and two zeros are$4$and$3+i$.

Step 2. Concept

Conjugate Pair Theorem says that if a polynomial with degree $n$with real coefficient, has one complex zero of the form $a+bi$then the polynomial should have the conjugate pair of $a+ib$that is$a-ib$ as another zero.

Step 3. Explanation

Since $f\left(x\right)$has coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that $3-i$, the conjugate of $3+i$, is the remaining zero.