Maharashtra Board Class 10 Math Part 1 Solution Chapter 2 Practice Set 2.2 – Quadratic Equations
Balbharati Maharashtra Board Class 10 Math Part 1 Solution Chapter 2: Quadratic Equations. Marathi or English Medium Students of Class 10 get here Quadratic Equations full Practice set Solution.
Std |
Maharashtra Class 10 |
Subject |
Math Part 1 Solution |
Chapter
Practice set |
Quadratic Equations
2.2 |
Practice set 2.2
(1) Solve the following quadratic equations by factorization.
(1) x^{2} – 15x + 54 = 0
Or, x^{2} – 6x – 9x + 54 = 0
Or, x (x – 6) – 9 (x – 6) = 0
Or, (x – 6) (x – 9) = 0
∴ Either, x – 6 = 0
Or, x = 6
Or, x – 9 = 0
Or, x = 9
Are the roots of the equation.
(2) x^{2} + x – 20 = 0
Or, x^{2} + 5x – 4x – 20 = 0
Or, x (x + 5) – 4 (x + 5) = 0
Or, (x + 5) (x – 4) = 0
Either, x + 5 = 0
or, x = -5
Or, x – 4 = 0
or, x = 4
One the 0 root of the equation
(3) 2y^{2} + 27y + 13 = 0
Or, 2y^{2} + y + 26y + 13 = 0
Or, y (2y + 1) + 13 (2y + 1) = 0
Or, (2y + 1) (y + 13) = 0
Either, 2y + 1 = 0
Or, y = -1/2
Or, y + 13 = 0
Or, y = -13
one the roots of the equation.
(4) 5m^{2} = 22m + 15
Or, 5m^{2} – 22m – 15 = 0
Or, 5m^{2} – 25m + 3m – 15 = 0
Or, 5m (m – 5) + 3 (m – 5) = 0
Or, (m – 5) (5m + 3) = 0
Either m – 5 = 0
Or, m = 5
Or, 5m + 3 = 0
Or, m = 3/5
Are the roots of the equation
(5) 2x^{2} – 2x + ½ = 0
Or, 2x^{2} – x – x + ½ = 0
Or, 2x ( – ½) – 1 (x – ½) = 0
Or, (x – ½) (2x – 1) = 0
Either, x – 1/2 = 0
Or, x = 1/2
Or, 2x – 1 = 0
Or, x = 1/2
Are the roots of the equation
(6) 6x – 2/x = 1
Or, 6x – 2/x – 1 = 0
Multiplying x —- both sides we get,
6x^{2} – 2/x × x – 1 × x = 0
Or, 6x^{2} – x – 2 = 0
Or, 6x^{2} + 3x – 4x – 2 = 0
Or, 3x (2x + 1) – 2 (2x + 1) = 0
Or, (2x + 1 (3x – 2) = 0
Either, 2x + 1 = 0
Or, x = -1/2
Or, 3x – 2 = 0
Or, x = 2/3
Are the roots of the equation
(7) √2 x^{2} + 7x + 5√2 = 0 to solving this equation by factorisation, complete the following activity.
Solution:
√2 x^{2}+ 7x + 5√2 = 0
Or, √2 x^{2} + 5 2x + 5x + 5√2 = 0
Or, √2 x (x + √2) + 5 (x + √2) = 0
Or, (x + √2) (√2 x + 5) = 0
Either, x + √2 = 0
Or, x = -√2
Or, √2 x + 5 = 0
Or, x = -5/√2
Are the roots of the equation.
(8) 3x^{2} – 2√6 x + 2 = 0
Or, 3x^{2} – √6x – √6x + 2 = 0
Or, √3x (√3x – √2) – √2 (√3x – √2) = 0
Or, (√3x – √2) (√3x – √2) = 0
∴ √3x – √2 = 0
Or, x = √2/√3, √2/3 Are the roots of equation
(9) 2m (m – 24) = 50
Or, 2m^{2} – 48m – 50 = 0
Or, 2m^{2} – 50m + 2m – 50 = 0
Or, 2m (m – 25) + 2 (m – 25) = 0
Or, (m – 25) (2m + 2) = 0
Either,
m – 25 = 0
Or, m = 25
Or, 2m + 2 = 0
Or, m = 1
Are the roots of the equation.
(10) 25m^{2} = 9
Or, 25m^{2} – 9 = 0
Or, (5m)^{2} – (3)^{2} = 0
Or, (5m + 3) (5m – 3) = 0 [∵ a^{3 }– b^{2} = (a + b) (a – b)]
Either, 5m + 3 = 0
Or, m = -3/5
Or, 5m – 3 = 0
Or, m = 3/5
Are the roots of equation
(11) 7m^{2} = 21m
Or 7m^{2} – 21m = 0
Or, 7m (m – 3) = 0
Either, 7m = 0
Or, m = 0
Or, m – 3 = 0
Or, m = 3
Are the roots of the equation
(12) m^{2} – 11 = 0
Or, m^{2} – (√11)^{2} = 0
Or, (m + √1) (m – √11) = 0 [∵ a^{2} – b^{2} = (a + b) (a – b)]
Either, m + √11 = 0
Or, m = – √11
Or, m – √11 = 0
Or, m = √11
Are the roots of equation
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