Question

find the roots of the quadratic equation by factorisation 2x2-x-6=0

Answer 1

$2 {x}^{2} - x - 6 = 0 \\ \\ \\ = > 2 {x}^{2} - (4 - 3)x - 6 = 0 \\ \\ \\ = > 2 {x}^{2} - 4x + 3x - 6 = 0 \\ \\ = >2x(x - 2) + 3(x - 2) = 0 \\ \\ \\ = > (x - 2)(2x + 3) = 0 \\ \\ \\ \\ \\ \\ \boxed{ \bold{ \underline{x = 2 \: \: \: \: \: \: \: \: or \: \: \: \: x = \: - \frac{3}{2} }}}$

Answer 2

2X^2 - X - 6 = 0
given equation is a quadratic equation ,use
X = -B+- √(B^2 - 4 AC )/ 2A

HERE A = 2 ,B = -1 , C = -6

X = -(-1) +- √ {( -1)^2 - 4 ( 2) (-6) } /2 (2)

X = 1 +- √ {1+48} /4

X = 1 +- √ 49 / 4

X = 1+- 7 / 4

X = 1+7 /4 ,1-7 /4

X = 8/4 ,-6 /4

X = 2 ,-3/2

X = 2 , X = -3/2
(X- 2), 2X = -3.
(X- 2) ,(2X + 3 )

hence ,X - 2) (2 X +3 ) are the factors of given equation.

hope it helps !
than you !