Find the roots of the following quadratic equation by factorisation:
$2x^{2} + x - 6 = 0$

(A) To find the roots of the quadratic equation $2x^{2} + x - 6 = 0$ by factorisation,we split the middle term.
We need two numbers whose product is $2 \times (-6) = -12$ and whose sum is $1$.
These numbers are $4$ and $-3$.
So,$2x^{2} + 4x - 3x - 6 = 0$.
Grouping the terms,we get $2x(x + 2) - 3(x + 2) = 0$.
Factoring out $(x + 2)$,we have $(x + 2)(2x - 3) = 0$.
Setting each factor to zero:
$x + 2 = 0 \implies x = -2$
$2x - 3 = 0 \implies 2x = 3 \implies x = \frac{3}{2}$.
Thus,the roots are $x = -2$ and $x = \frac{3}{2}$.