Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $1-6$, solve each equation.

$2x^2-x=0$.

Step-by-Step Solution

Answer

The solution set for the equation $2x^2-x=0$ is, $\left\{0,\frac{1}{2}\right\}$.

Step 1 Given equation is,

$2x^2-x=0$

First factor out the common terms.

$2x^2-x=x\left(2x-1\right)$

Step 2 Now use the zero product property and simplify it.

$$\begin{gathered} x\left(2x-1\right)=0 \\ x=0 and 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}$$

So, the required solution set is, $\left\{0,\frac{1}{2}\right\}$.