Question

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

Answer 1

Solve for $x$:

The given equation is $6x^2-x-2=0$

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

$\Rightarrow$$2x\left(3x-2\right)+1\left(3x-2\right)=0$

$\Rightarrow$ $\left(3x-2\right)\left(2x+1\right)=0$

$\Rightarrow$ $3x-2=0,2x+1=0$

$\therefore x=\frac{2}{3},-\frac{1}{2}$

Hence, the roots of the given equation are $\frac{2}{3}$ and $-\frac{1}{2}$.