Question

Without solving the quadratic equation $6x^2-x-2=0,$ find whether $x=\frac{2}{3}$ is a solution of this equation or not.

Answer 1

Step : Check whether $x=\frac{2}{3}$ is a solution to the equation $6x^2-x-2=0$ or not
For $x=\frac{2}{3}$ to be solution of the given quadratic equation it should satisfy the equation
$6x^2-x-2=0$
Put $x=\frac{2}{3}$ in L.H.S.
L.H.S. $=6{\left(\frac{2}{3}\right)}^2-\left(\frac{2}{3}\right)-2$
$=\frac{24}{9}-\frac{2}{3}-2$
$=\frac{24-6-18}{9}$
$=0$
$=R.H.S.$
Since $L.H.S.=R.H.S$, then $x=\frac{2}{3}$is a solution of the given equation.