Find the roots of the following quadratic equations by factorisation:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(i) X2 – 3x – 10
= x2 – 5x +2x – 10
= x(x – 5 ) + 2(x – 5 )
= (x – 5 )(x+2)
Roots of this equation are the values for which (x – 5 )(x+2) = 0
∴ x-5 = 0 or x+2 = 0
i.e.,
x = 5 or x = -2
(ii) 2x2 + x – 6
= 2x2 + 4x – 3x – 6
= 2x (x+2) – 3(x+2)
= (x+2)(2x – 3 )
Roots of this equation are the values for which (x+2)(2x – 3) = 0
∴ x+ 2= 0 or 2x – 3 = 0
x = −2 or x = 
(iii) 
Roots of this equation are the values for which 
= 0
∴ 
= 0 or 
= 0
i.e., x = 
or x = 
(iv) 
Roots of this equation are the values for which (4x – 1 )2 = 0
Therefore,
(4x – 1 ) = 0 or (4x – 1) = 0
i.e., 
(v) 100x2 – 2x +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
Therefore,
(10x – 1) = 0 or (10x – 1) = 0
i.e., 