Question

Find the roots of quadratic equations by factorisation:

(i) √2 x2 + 7x + 5√2=0

(ii) 100x2 – 20x + 1 = 0​

Answer 1

(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

⭐ＳＯＬＵＴＩＯＮ:

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1.√2x²+7x+5√2=0

→ √2x²+5x+2x+5√2=0

→ x(√2x+5) +√2(√2x+5) =0

→ (x+√2) (√2x+5) =0

→ (x+√2) =0 OR (√2x+5) =0

→ x= -√2 OR -5/√2

Therefore, (-√2, -5/√2) are the roots.

2. 100x²-20x+1=0

→ 100x²-10x-10x+1=0

→ 10x(10x-1) -1(10x-1) =0

→(10x-1) ((10x-1) =0

→ (10x-1) =0 OR (10x-1) =0

→ x=1/10 OR x= 1/10

Therefore, The roots are (1/10 , 1/10)