Question

Find the roots of quadratic equations by factorisation:

(i) √2 x2 + 7x + 5√2=0

(ii) 100x2 – 20x + 1 = 0


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Answer 1

Answer:

(i) √2 x2 + 7x + 5√2=0

Considering the L.H.S. first,

⇒ √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 (√2x + 5)(x + √2) = 0

Therefore, √2x + 5 = 0 or x + √2 = 0

⇒ x = -5/√2 or x = -√2

(ii) Given, 100x2 – 20x + 1=0

Considering the L.H.S. first,

⇒ 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

Therefore,

(10x – 1) = 0

or (10x – 1) = 0

⇒ x =1/10 or x =1/10

Answer 2

(i) √2 x2 + 7x + 5√2

= √2 x2 + 5x + 2x + 5√2

= x (√2x + 5) + √2(√2x + 5)

= (√2x + 5)(x + √2)

Roots of this equation are the values for which (√2x + 5)(x + √2) = 0

∴ √2x + 5 = 0 or x + √2 = 0

⇒ x = -5/√2 or x = -√2

(ii)100x2 – 20x + 1

= 100x2 – 10x - 10x + 1

= 10x(10x - 1) -1(10x - 1)

= (10x - 1)2

Roots of this equation are the values for which (10x - 1)2 = 0

∴ (10x - 1) = 0 or (10x - 1) = 0

⇒ x = 1/10 or x = 1/10

Hope it helps !!