Find the roots of the following Quadratic Equations by factorization.

(i)x²-3x-10 = 0
x²-5x+2x-10 = 0
x(x-5)+2(x-5) = 0
(x-5)(x+2) = 0
⇒ x-5 = 0 or, x+2 = 0
x = 5 or x =-2
Hence the required roots are 5, -2.

(ii)2x²+x-6 = 0
2x²+4x-3x-6 = 0
2x(x+2)-3(x+2) = 0
(2x-3)(x+2) = 0
⇒ 2x-3 = 0 or, x+2 = 0
x = 3/2 or x = -2
Hence the required roots are 3/2 , -2.

(iii)√2x²+7x+5√2 = 0
√2x²+2x+5x+ 5√2 = 0
√2x(x+√2)+5(x+√2) = 0
(x+√2)(√2x +5) = 0
⇒ x+√2 = 0 or, √2x +5 = 0
x = -√2 or x = –5/√2

Hence the required roots are -√2, –5/√2.

(iv)2x²-x+1/8=0
16x²-8x+1 = 0
(4x)²-2.4x.1+12 = 0
(4x-1)2= 0
⇒ 4x-1 = 0  or 4x-1 = 0
x = 1/4   or x = 1/4
Hence the required roots are 1/4 , 1/4

(v)100x²-20x+1 = 0
(10x)²-2×10x.1+12= 0
(10x-1)² = 0
10x-1 = 0 or 10x-1 = 0
x = 1/10 or x = 1/10
Hence the required roots are 1/10  or 1/10