Answer :
(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) 2 x2 + 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
(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 – 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
Therefore,
(10x – 1) = 0 or (10x – 1) = 0
i.e.,
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