Chapter 4.7, Problem 5OE

To determine

To solve the equation.

Answer to Problem 5OE

The values of $y=0,2$

Explanation of Solution

Given information:

  $y^2-2y=0$

Calculation:

The given equation already has 0 as one side, and the other side is already factored. Simply set each factored equal to 0 and solve.

The equationcan be calculated as

  $\begin{array}{l}{y}^2-2y=0\\ y\left(y-2\right)=0\left[\text{take the common factor,}y\right]\end{array}$

Therefore,

  $\begin{array}{l}y\text{=0 or }\left(y-2\right)=0\left[\text{use the zero-product property}\right]\\ y=0\text{ or }y=2\\ \\ \text{check: }f\left(0\right)=0\left(0-2\right)=0\\ f\left(2\right)=2\left(2-2\right)=2\left(0\right)=0\end{array}$

Hence,

The values of $y=0,2$