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

⇒ 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 = 3/2

(III) √2 x2 + 7x + 5√2

= √2 x2 + 5x + 2x + 5√2

= x (√2x + 5) + √2(√2x + 5)= (√2x + 5)(x + √2)

Roots of this equation are the values for which (√2x + 5)(x + √2) = 0

∴ √2x + 5 = 0 or x + √2 = 0

⇒ x = -5/√2 or x = -√2

(iv) 2x2 – x + 1/8

= 1/8 (16x2 - 8x + 1)

= 1/8 (16x2 - 4x -4x + 1)

= 1/8 (4x(4x - 1) -1(4x - 1))

= 1/8(4x - 1)2

Roots of this equation are the values for which (4x - 1)2 = 0

∴ (4x - 1) = 0 or (4x - 1) = 0

⇒ x = 1/4 or x = 1/4

(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

∴ (10x - 1) = 0 or (10x - 1) = 0

⇒ x = 1/10 or x = 1/10