Find the roots of the following quadratic equations by factorisation:
(i) √2 x2 + 7x + 5√2 = 0
(ii) 2x2 – x +1/8 = 0
(iii) 100x2 – 20x + 1 = 0
(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