Find the roots of the quadratic equation 3 x 2 - 2 6 x + 2 = 0 .

Given, 3 x 2 - 2 6 x + 2 = 0 Splitting the middle term, we get: 3 x 2 - 2 6 x + 2 = 3 x 2 - 6 x - 6 x + 2 = 3 x 3 x - 2 - 2 3 x - 2 = 3 x - 2 3 x - 2 So, the roots of the equation are the values of x for which 3 x - 2 3 x - 2 = 0 Now, 3 x - 2 = 0 for x = 2 3 . So, this root is repeated twice, one for each repeated factor 3 x - 2 . Therefore, the roots of 3 x 2 - 2 6 x + 2 = 0 are 2 3 , 2 3 .

E M B I B E

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 4

EASY

10th Uttar Pradesh Board

IMPORTANT

Earn 100

Check whether the following is a quadratic equation:

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

Important Questions on Quadratic Equations

EASY

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 5

Check whether the following is a quadratic equation:

{(x + 2)}^{3} = x^{3} - 4

EASY

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 6

Check whether the following is a quadratic equation:

x (2 x + 3) = x^{2} + 1

MEDIUM

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 7

Find the roots of the equation

2 x^{2} - 5 x + 3 = 0

, by factorisation.

MEDIUM

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 8

Find the roots of the quadratic equation

6 x^{2} - x - 2 = 0

.

MEDIUM

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 9

Find the roots of the quadratic equation

3 x^{2} - 2 \sqrt{6} x + 2 = 0

.

MEDIUM

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 10

A charity trust decides to build a prayer hall having a carpet area of $300 m^{2}$ with its length one metre more than twice its breadth. What should be the length and breadth of the hall?

MEDIUM

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 11

Solve the equation $2 x^{2} - 5 x + 3 = 0$ by the method of completing the square.

MEDIUM

10th Uttar Pradesh Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 4 - Quadratic Equations>Exercise 4>Q 12

Find the roots of the equation