Question:

Find the roots of the quadratic equation $2 x^{2}-x-6=0$.

Solution:

The given quadratic equation is $2 x^{2}-x-6=0$.

$2 x^{2}-x-6=0$

$\Rightarrow 2 x^{2}-4 x+3 x-6=0$

$\Rightarrow 2 x(x-2)+3(x-2)=0$

$\Rightarrow(x-2)(2 x+3)=0$

$\Rightarrow x-2=0$ or $2 x+3=0$

$\Rightarrow x=2$ or $x=-\frac{3}{2}$

Hence, the roots of the given equation are 2 and $-\frac{3}{2}$.