Chapter 4.3, Problem 16AYU

To determine

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

Answer to Problem 16AYU

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

Explanation of Solution

Given:

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

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

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

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