Solve 4 x - 3 = 5 2 x + 3 , x ≠ 0 , x ≠ - 3 2

We have, 4 x - 3 = 5 2 x + 3 ⇒ 4 - 3 x x = 5 2 x + 3 ⇒ 4 - 3 x 2 x + 3 = 5 x ⇒ 8 x + 12 - 6 x 2 - 9 x = 5 x ⇒ - 6 x 2 - 6 x + 12 = 0 ⇒ x 2 + x - 2 = 0 ⇒ x 2 + 2 x - x - 2 = 0 ⇒ x x + 2 - 1 x + 2 = 0 ⇒ x - 1 x + 2 = 0 ⇒ x - 1 = 0 or x + 2 = 0 ⇒ x = 1 or x = - 2 Therefore, x = 1 , - 2 .

Solve the equation 1 x + 4 - 1 x - 7 = 11 30 , x ≠ - 4 , 7

We have, 1 x + 4 - 1 x - 7 = 11 30 ⇒ x - 7 - x - 4 ( x + 4 ) ( x - 7 ) = 11 30 ⇒ - 11 x 2 - 3 x - 28 = 11 30 ⇒ - 1 x 2 - 3 x - 28 = 1 30 ⇒ x 2 - 3 x - 28 = - 30 ⇒ x 2 - 3 x + 2 = 0 ⇒ x 2 - 2 x - x + 2 = 0 ⇒ x x - 2 - 1 x - 2 = 0 ⇒ x - 1 x - 2 = 0 ⇒ x - 1 = 0 or x - 2 = 0 ⇒ x = 1 or x = 2 Therefore, x = 1 , 2 .

E M B I B E

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 3

MEDIUM

10th CBSE

IMPORTANT

Earn 100

Find the roots of the quadratic equation:
$2 x^{2} - 7 x + 3 = 0$

Important Questions on Quadratic Equations

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 4

The sum of the squares of two consecutive natural numbers is $421 .$ Find the numbers.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 5

Solve the following equation:

$\frac{2 x}{x - 3} + \frac{1}{2 x + 3} + \frac{3 x + 9}{(x - 3) (2 x + 3)} = 0; x \neq 3, - \frac{3}{2}$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 6

Solve

$\frac{4}{x} - 3 = \frac{5}{2 x + 3}, x \neq 0, x \neq - \frac{3}{2}$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 7

The sum of the reciprocals of Rehman's ages (in years)

3

years ago and

5

years from now is

\frac{1}{3}

. Find his present age.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 8

Solve the equation

$\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq - 4, 7$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 9

If one root of the quadratic equation

x^{2} - 5 x + 6 k = 0

is reciprocal of other, find the value of

k

.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 10

An express train takes

1

hour less than a passenger train to travel

132 km

between stations

A

and

B

(without taking into consideration the time they stop at intermediate stations. If the average speed of the express train is

11 km / hour

more than that of the passenger train, find the average speed of the two trains.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 11

If two pipes function simultaneously, a reservoir will be filled in twelve hours. First pipe fills the reservoir $10$ hours faster than the second pipe. If the second pipe will take $k$ hours to fill the reservoir, then find the value of $k$ .