Question:

Solve the following quadratic equations by factorization.

(1) x2 – 15x + 54 = 0

(2) x2 + x – 20 = 0

(3) 2y2 + 27y + 13 = 0

(4) 5m2 = 22m + 15

(5) 2x2 – 2x + ½ = 0

(6) 6x -2/x = 1

(7) √2 x2 + 7 x + 5 √2 = 0 to solve this quadratic equation by factorization, complete the following activity.

(8) 3x2 – 2 √6 x + 2 = 0

(9) 2m (m-24) = 50

(10) 25m2 = 9

(11) 7m2 = 21m

(12) m2 – 11 = 0

Answer:

(1) x2 – 15x + 54 = 0

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 10

(2) x2 + x – 20 = 0

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 11

(3) 2y2 + 27y + 13 = 0

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 12

(4) 5m2 = 22m + 15

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 13

(5) 2x2 – 2x + ½ = 0

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 14

(2x – 1) (2x – 1)

2x – 1 = 0

x = ½, ½

Hence x = ½, ½ are the roots of the equation

(6) 6x -2/x = 1

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 15

(7) √2 x2 + 7 x + 5 √2 = 0 to solve this quadratic equation by factorization, complete the following activity.

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 16

(8) 3x2 – 2 √6 x + 2 = 0

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 17

(9) 2m (m-24) = 50

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 18

(10) 25m2 = 9

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 19

(11) 7m2 = 21m

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 20

(12) m2 – 11 = 0

Solution:

Maharashtra Board Solutions for Class 10 Maths Part 1 Chapter 2 - Image 21

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