Chapter 2 Quadratic Equations Set 2.2

Question 1.
Solve the following quadratic equations by factorisation.
i. x2 – 15x + 54 = 0
ii. x2 + x – 20 = 0
iii. 2y2 + 27y + 13 = 0
iv. 5m2 = 22m + 15

vii. √2x2 + 7x + 5√2 = 0 to solve this quadratic equation by factorisation complete the following activity
viii. 3x2 – 2√6x + 2 = 0
ix. 2m(m – 24) = 50
x. 252 = 9
xi. 7m2 = 21 m
xii. m2 – 11 = 0
Solution:

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 1

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ x – 9 = 0 or x – 6 = 0
∴ x = 9 or x = 6
∴ The roots of the given quadratic equation are 9 and 6.

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 2
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ x + 5 = 0 or x – 4 = 0
∴ x = -5 or x = 4
∴ The roots of the given quadratic equation are -5 and 4.

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 3
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
word image 7252 5

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 4
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
word image 7252 7

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 5

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 6
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
word image 7252 10

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 7
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 8

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 9
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 10

ix. 2m (m – 24) = 50
∴ 2m2 – 48m = 50
∴ 2m2 – 48m – 50 = 0
∴m2 – 24m – 25 = 0 …[Dividing both sides by 2]
Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 11
∴ m – 25 = 0 or m + 1 = 0
∴ m = 25 or m = -1
∴ The roots of thes given quadratic equation are 25 and -1.

x. 25m2 = 9
∴ 25m2 – 9 = 0
∴ (5m)2 – (3)2 = 0
∴ (5m + 3) (5m – 3) = 0
…. [∵a2 – b2 = (a + b) (a – b)]
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
word image 7252 16

xi. 7m2 = 21m
∴ 7m– 21m = 0
∴ m2 – 3m = 0 …[Dividing both sides by 7]
∴ m(m – 3) = 0
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ m = 0 or m – 3 = 0
∴ m = 0 or m = 3
∴ The roots of the given quadratic equation are 0 and 3.

Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.2 12
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ m + √11 = 0 or m – √11 = 0
∴ m = -√11 or m = √11
∴ The roots of the given quadratic equation are – √11 and √11