Question

find the roots of the following quadratic equations by factorisation......
1. x2 -- 3x -- 10= 0
2. 2x2 + x -- 6=0

Answer 1

1) x2 - 3x -10=0
x2-5x +2x -10=0
x(x-5)+2(x-5)=0
(x+2)(x-5)=0
x=-2,5
hence it's roots r -2&5
2) 2x2+x-6=0
2x2+4x-3x-6=0
2x(x+2)-3(x+2)=0
(2x-3)(x+2)=0
x=3/2,-2

Answer 2

: Required Answer

$\longrightarrow$ (i) Given, x2 – 3x – 10 =0

Taking LHS,

=>x2 – 5x + 2x – 10

=>x(x – 5) + 2(x – 5)

=>(x – 5)(x + 2)

The roots of this equation, x2 – 3x – 10 = 0 are the values of x for which (x – 5)(x + 2) = 0

Therefore, x – 5 = 0 or x + 2 = 0

=> x = 5 or x = -2

$\longrightarrow$(ii) Given, 2x2 + x – 6 = 0

Taking LHS,

=> 2x2 + 4x – 3x – 6

=> 2x(x + 2) – 3(x + 2)

=> (x + 2)(2x – 3)

The roots of this equation, 2x2 + x – 6=0 are the values of x for which (x – 5)(x + 2) = 0

Therefore, x + 2 = 0 or 2x – 3 = 0

=> x = -2 or x = 3/2