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

Balbharti Maharashtra State Board Class 10 Maths Solutions covers the Practice Set 2.2 Algebra 10th Class Maths Part 1 Answers Solutions Chapter 2 Quadratic Equations.

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

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
v. 2x2 – 2x + \(\frac { 1 }{ 2 } \) = 0
vi. 6x – \(\frac { 2 }{ x } \) = 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:
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
∴ y + 13 = 0 or 2y + 1 = 0
∴ y = – 13 or 2y = -1
∴ y = -13 or y = –\(\frac { 1 }{ 2 } \)
∴ The roots of the given quadratic equation are -13 and – \(\frac { 1 }{ 2 } \)

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
∴ m – 5 = 0 or 5m + 3 = 0
∴ m = 5 or 5m = -3
∴ m = 5 or m = \(\frac { -3 }{ 5 } \)
∴ The roots of the given quadratic equation are 5 and – \(\frac { 3 }{ 5 } \)

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
∴ 3x – 2 = 0 or 2x + 1 = 0
∴ 3x = 2 or 2x = -1
∴ x = \(\frac { 2 }{ 3 } \) or 2x = -1
∴ The roots of the given quadratic equation are \(\frac { 2 }{ 3 } \) and \(\frac { -1 }{ 2 } \).

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
∴ 5m + 3 = 0 or 5m – 3 = 0
∴ 5m = -3 or 5m = 3
∴ m = \(\frac { -3 }{ 5 } \) or m = \(\frac { 3 }{ 5 } \)
∴ The roots of the given quadratic equation are \(\frac { -3 }{ 5 } \) and \(\frac { 3 }{ 5 } \).

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.

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

Leave a Comment

Scroll to Top