Question

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Find the roots of the following quadratic equations by factorisation:

(i) x2 -3x – 10 = 0

(ii) 2x2 + x – 6 = 0

(iii) √2x2 + 7x + 5√2 = 0


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Answer 1

Answer:

(i) √2 x2 + 7x + 5√2=0

Taking LHS,

=> √2 x2 + 5x + 2x + 5√2

=> x (√2x + 5) + √2(√2x + 5)= (√2x + 5)(x + √2)

The roots of this equation, √2 x2 + 7x + 5√2=0 are the values of x for which (x – 5)(x + 2) = 0

Therefore, √2x + 5 = 0 or x + √2 = 0

=> x = -5/√2 or x = -√2

(ii) 2x2 – x +1/8 = 0

Taking LHS,

=1/8 (16x2 – 8x + 1)

= 1/8 (16x2 – 4x -4x + 1)

= 1/8 (4x(4x – 1) -1(4x – 1))

= 1/8 (4x – 1)2

The roots of this equation, 2x2 – x + 1/8 = 0, are the values of x for which (4x – 1)2= 0

Therefore, (4x – 1) = 0 or (4x – 1) = 0

⇒ x = 1/4 or x = 1/4

(iii) Given, 100x2 – 20x + 1=0

Taking LHS,

= 100x2 – 10x – 10x + 1

= 10x(10x – 1) -1(10x – 1)

= (10x – 1)2

The roots of this equation, 100x2 – 20x + 1=0, are the values of x for which (10x – 1)2= 0

∴ (10x – 1) = 0 or (10x – 1) = 0

⇒ x = 1/10 or x = 1/10

Answer 2

x² - 3x - 10 = 0

x² - 5x + 2x - 10 = 0

(x - 5) (x + 2) = 0

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2x² + x - 6 = 0

2x² + 4x - 3x - 6 = 0

(x + 2) (2x + 2) = 0

▬▬▬▬▬

√2x² + 7x + 5√2 = 0

√2x² + 5x + 2x + 5√2 = 0

x(√2x + 5) + √2(√2x + 5) = 0

(√2x + 5) (x + √2) = 0

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