Q1: Find the roots of the following quadratic equations by factorization:

Q1: Find the roots of the following quadratic equations by factorization:

(i) x² – 3x – 10 = 0

(ii) 2x² + x – 6 = 0

(iii) √2 x² + 7 x + 5√2 = 0

(iv) 2x² – x + 1/8 = 0

(v) 100 x² – 20x + 1 = 0

 Answer:

x² – 3x – 10 = 0

So we can write middle term as -3x = -5x + 2x

x² – 5x + 2x – 10 = 0

    x(x - 5) + 2(x - 5) = 0

    (x - 5)(x + 2) = 0

x - 5 = 0  and x + 2 = 0

x = 5 and x = -2

  5 and -2  are our required root of quadratic equation.

(ii) 2x² + x – 6 = 0

    2x² + 4x – 3x – 6 = 0

2x(x + 2) – 3(x + 2) = 0

(x + 2)(2x – 3) = 0

    x + 2 = 0   and  2x – 3 = 0

x = –2  and x = 3/2

–2 and 3/2  are our required root of quadratic equation.

(iii) √2 x² + 7x + 5√2 = 0

Similarly multiply √2 with 5√2   and we get 10

Pairs of 10 are

1*10 = 10       sum  1+ 10 = 11

2*5 = 10                     sum 2+ 5 = 7

So our required pair is 2 and 5

    √2 x² + 5x + 2x + 5√2 = 0

x (√2x + 5) + √2(√2x + 5) = 0

(√2x + 5)(x + √2) = 0

     √2x + 5 = 0 and  x + √2 = 0

x = –5/√2  and x = –√2

–5/√2 and  –√2  are our required root of quadratic equation.

(iv) 2x² – x + 1/8 = 0

Multiply by 8 we get

16x² – 8x + 1 = 0
(V)100 x² – 20x + 1 = 0