Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

find the real solutions of each equation.

$3x^2-x=0$

Step-by-Step Solution

Answer

The solutions of the equation $3x^2-x=0$ are

$$\begin{gathered} x=0 \\ x=\frac{1}{3} \end{gathered}$$

Step 1. Given data

The given equation is 

$3x^2-x=0$

Step 2. solution of equation

Factorize the equation

$$\begin{gathered} 3x^2-x=0 \\ x\left(3x-1\right)=0 \end{gathered}$$

Use zero product property

 $$\begin{gathered} 3x-1=0 \\ 3x=1 \\ x=\frac{1}{3} \end{gathered}$$

and $x=0$

solution of the equation are $x=0 \& \frac{1}{3}$

Step 3. Verification

Substitute $0$ for x in the equation 

$$\begin{gathered} 3x^2-x=0 \\ 3{\left(0\right)}^2-\left(0\right)\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$

Substitute $\frac{1}{3}$for x in the equation 

$$\begin{gathered} 3x^2-x=0 \\ 3{\left(\frac{1}{3}\right)}^2-\left(\frac{1}{3}\right)\stackrel{?}{=}0 \\ \frac{1}{3}-\frac{1}{3}\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$

Both sides of the equation are the same for both solutions so the solution is correct.