Chapter 4.3, Problem 15AYU

To determine

To find: The remaining zeros of the polynomial function $f\left(x\right)$ whose coefficients are real numbers.

Answer to Problem 15AYU

$\text{Complex conjugate }2-i,-3+i\text{ are the remaining zero of polynomial function }f\left(x\right)$.

Explanation of Solution

Given:

Degree $=6$, zeros $=2,2+i,-3-i,0$.

Since the degree $=6$ there will be 6 real zeros.

Since $2+i,-3-i$ are the complex zeros of the polynomial function $f\left(x\right)$ and $f\left(x\right)$ has coefficients that are real numbers Complex zero appear as conjugate pairs.

By the conjugate pair theorem $2+i,-3-i$ are the complex zeros of the polynomial function $f\left(x\right)$.

The complex conjugate of $2+i,-3-i=2-i,-3+i$ are also the zeros of polynomial function $f\left(x\right)$.