Chapter 4.7, Problem 14OE

To determine

To find: the zeroes of the function

Answer to Problem 14OE

The zeroes of the function is $y=\left\{0,-1,3\right\}$

Explanation of Solution

Given information: The function is $k\left(z\right)=z\left(z-3\right)\left(z+1\right)$

Calculation:

  $z\left(z-3\right)\left(z+1\right)=0$

The given equation already has $0$ as one side, and the other side is already factored

Simplify set each factor equal to $0$

  $\begin{array}{l}z-3=0\\ z=3\\ z+1=0\\ z=-1\\ z=0\\ k\left(0\right)=\left(0\right)\left(\left(0\right)-3\right)\left(\left(0\right)+1\right)=0\\ k\left(-1\right)=\left(-1\right)\left(\left(-1\right)-3\right)\left(\left(-1\right)+1\right)=0\\ k\left(3\right)=\left(3\right)\left(\left(3\right)-3\right)\left(\left(3\right)+1\right)=0\\ y=\left\{0,-1,3\right\}\end{array}$