Class 10 Maths 1 Practice Set 2.2 Solutions | Lesson no.2 Quadratic Equations | Maharashtra Board

Class 10 Maths 1 Practice Set 2.2 Solutions | Lesson no.2 Quadratic Equations  | Maharashtra Board 

Introduction

In this article, you will find complete step-by-step solutions to Practice Set 2.2 from Chapter 2 – Quadratic Equations. These solutions are prepared in a simple exam-oriented format for Maharashtra Board Class 10 students.

1. Solve the following quadratic equations by factorisation.

1. x² − 15x + 54 = 0

Solution 

x²−9x−6x+54=0

x(x−9)−6(x−9)=0

(x−9)(x−6)=0

x-9=0 or x-6=0

X=9 or X=6

Answer: x = 9, 6

2. x² + x − 20 = 0

Solution

x²+5x−4x−20=0

x(x+5)−4(x+5)=0

(x+5)(x−4)=0

X+5=0 or X-4=0

X=-5 or X=4

Answer: x = −5, 4

3. 2y² + 27y + 13 = 0

Solution

2y²+26y+y+13=0

2y(y+13)+1(y+13)=0

(y+13)(2y+1)=0

y+13=0   or   2y+1=0

y = −13,   or  2y=−1

y = −13,    or. y= −1/2

Answer: y = −13, −1/2

4. 5m² = 22m + 15

Solution

5m²−22m−15=0

5m²+3m−25m−15=0

m(5m+3)−5(5m+3)=0

(5m+3)(m−5)=0

5m+3=0 or m−5=0

5m=-3 or m=5

m=-3/5 or m=5

Answer: m = 5, −3/5

5. 2x² − 2x + 1/2 = 0

Solution

Multiply by 2:

4x²−4x+1=0

(2x−1)²=0

Answer: x = 1/2

6. 6x − 2/x = 1

Solution

Multiply by x:

6x²−x−2=0

6x²−4x+3x−2=0

2x(3x−2)+(3x−2)=0

(3x−2)(2x+1)=0

Answer: x = 2/3, −1/2

8.   3x² − 2√6x + 2 = 0

Solution

3x² − 2√6x + 2 = 0

∴ 3x² − √6x − √6x + 2 = 0

∴ √3x (√3x − √2) − √2 (√3x − √2) = 0

∴ (√3x − √2)(√3x − √2) = 0

∴ √3x − √2 = 0 or √3x − √2 = 0

∴ √3x = √2 or √3x = √2

∴ x = √2/√3 or x = √2/√3

∴ √2/√3 and √2/√3 are the roots of the equation.

9.    2m(m − 24) = 50

Solution

2m² − 48m = 50

∴ 2m² − 48m − 50 = 0

∴ 2m² − 50m + 2m − 50 = 0

∴ 2m(m − 25) + 2(m − 25) = 0

∴ (m − 25)(2m + 2) = 0

∴ m − 25 = 0 or 2m + 2 = 0

∴ m = 25 or m = −1

∴ 25 and −1 are the roots of the equation.

10.    25m² = 9

Solution

25m² − 9 = 0

∴ (5m)² − (3)² = 0

∴ (5m + 3)(5m − 3) = 0

∴ 5m + 3 = 0 or 5m − 3 = 0

∴ m = −3/5 or m = 3/5

∴ −3/5 and 3/5 are the roots of the equation.

11.  7m² = 21m

Solution

7m² − 21m = 0

∴ 7(m² − 3m) = 0

Dividing both sides by 7, we get

m² − 3m = 0

∴ m(m − 3) = 0

∴ m = 0 or m = 3

∴ 0 and 3 are the roots of the equation.

12.    m² − 11 = 0

Solution

m² − 11 = 0

∴ m² − (√11)² = 0

∴ (m + √11)(m − √11) = 0

∴ m + √11 = 0 or m − √11 = 0

∴ m = −√11 or m = √11

∴ −√11 and √11 are the roots of the equation.

Conclusion

Practice Set 2.2 helps students master solving quadratic equations using the factorisation method. Regular practice of these questions improves speed and accuracy in SSC Board examinations.

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Practice set 2.1