Find the roots of the following quadratic equations by factorisation: (i) x² - 3x - 10 = 0 (ii) 2x² + x - 6 = 0 (iii) √2x² + 7x + 5√2 = 0 (iv) 2x² - x + 18 = 0 (v) 100x² - 20x + 1 = 0

i) x² - 3x - 10 = 0 ⇒ x² - 5x + 2x - 10 = 0 ⇒ x(x - 5) + 2(x - 5) = 0 ⇒ (x + 2)(x - 5) = 0 ⇒ x = 5, -2
ii) 2x² + x - 6 = 0 ⇒ 2x² + 4x - 3x - 6 = 0 ⇒ 2x(x + 2) - 3(x + 2) = 0 ⇒ (x + 2)(2x - 3) = 0 ⇒ x = 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, -5/√2
iv) 2x² - x + 18 = 0 This quadratic equation does not factor easily and may not have real roots. The provided solution seems to have an error in this part.
v) 100x² - 20x + 1 = 0 ⇒ 100x² - 10x - 10x + 1 = 0 ⇒ 10x(10x - 1) - 1(10x - 1) = 0 ⇒ (10x - 1)(10x - 1) = 0 ⇒ x = 1/10, 1/10