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

Step-by-step explanation:

1. Given,

2

x

2

+7x+5

2

=0

or,

2

x

2

+2x+5x+5

2

=0

or, x

2

(x+

2

)+5(x+

2

)=0

or, (x

2

+5)(x+

2

)=0

⇒x=−

2

5

,−

2

.

These are the required roots.

2.Now,

100x

2

−20x+1=0

or, (10x)

2

−2.10x.1+1

2

=0

or, (10x−1)

2

=0

or, x=

10

1

,

10

1

.