Chapter 4.3, Problem 11AYU

To determine

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

Answer to Problem 11AYU

$\text{Complex conjugate }–i\text{ and }-2i\text{ are the remaining zeros of polynomial function }f\left(x\right)$.

Explanation of Solution

Given:

Degree $=5$, zeros $=1,i,2i$.

Since the degree $=5$ there will be 5 real zeros.

Since $i$ and $2i$ are the complex zero 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 $i$ and $2i$ are the complex zeros of the polynomial function $f\left(x\right)$.

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