Chapter 2: Q. 2 (page 126)

find the real solutions of each equation.
$3 x^{2} - x = 0$

Short Answer

Expert verified

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

$x = 0 x = \frac{1}{3}$

Step by step solution

Step 1. Given data

The given equation is

$3 x^{2} - x = 0$

Step 2. solution of equation

Factorize the equation

$3 x^{2} - x = 0 x (3 x - 1) = 0$

Use zero product property

$3 x - 1 = 0 3 x = 1 x = \frac{1}{3}$

and $x = 0$

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

Step 3. Verification

Substitute $0$ for x in the equation

$3 x^{2} - x = 0 3 {(0)}^{2} - (0) \overset{?}{=} 0 0 = 0$

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

$3 x^{2} - x = 0 3 {(\frac{1}{3})}^{2} - (\frac{1}{3}) \overset{?}{=} 0 \frac{1}{3} - \frac{1}{3} \overset{?}{=} 0 0 = 0$

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

find the real solutions of each equation.
$3 x^{2} - x = 0$

Short Answer

Step by step solution

Step 1. Given data

Step 2. solution of equation

Step 3. Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

find the real solutions of each equation.3x2-x=0

Short Answer

Step by step solution

Step 1. Given data

Step 2. solution of equation

Step 3. Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

find the real solutions of each equation.
$3 x^{2} - x = 0$