Maharashtra State Board Class 10 (SSC Board) Mathematics & Statistics Solutions Chapter 2 Quadratic Equations Practice Set 2.2 - Digest Answers | Maharashtra Board Solutions

Practice Set 2.2 Algebra 10th Std Maths Part 1 Answers Chapter 2 Quadratic Equations

Question 1 Maharashtra Board Solution

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 v. 2x2 – 2x + = 0 vi. 6x – = 1 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 & Step-by-Step Answer:

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.

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.

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ y + 13 = 0 or 2y + 1 = 0
∴ y = – 13 or 2y = -1
∴ y = -13 or y = –
∴ The roots of the given quadratic equation are -13 and –

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ m – 5 = 0 or 5m + 3 = 0
∴ m = 5 or 5m = -3
∴ m = 5 or m =
∴ The roots of the given quadratic equation are 5 and –

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ 3x – 2 = 0 or 2x + 1 = 0
∴ 3x = 2 or 2x = -1
∴ x = or 2x = -1
∴ The roots of the given quadratic equation are and .

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

ix. 2m (m – 24) = 50
∴ 2m²– 48m = 50
∴ 2m²– 48m – 50 = 0
∴m²– 24m – 25 = 0 …[Dividing both sides by 2]

∴ 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
∴ 5m + 3 = 0 or 5m – 3 = 0
∴ 5m = -3 or 5m = 3
∴ m = or m =
∴ The roots of the given quadratic equation are and .

xi. 7m²= 21m
∴ 7m²– 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.

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

Chapter 2 Quadratic Equations Practice Set 2.2 Solutions