Determine whether the given values of x is the solution of the gi… - Vidyadip

Question

Determine whether the given values of x is the solution of the given quadratic equation below:
$6 x^2-x-2=0 ; x=\frac{2}{3},-1$

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Answer

$6 x^2-x-2=0 ; x=\frac{2}{3},-1$
Now put $x = -1$ in $\text{L.H.S.}$ of equation.
$\text { L.H.S. }=6 \times(-1)^2-(-1)-2$
$ =6+1-2 $
$ =7-2=5 \neq 0 \neq \text { R.H.S. }$
Hence, $x = -1$ is not a root of the equation.
Put $x=\frac{2}{3}$ in $\text{L.H.S.}$ of equation.
$\text { L.H.S. }=6 \times\left(\frac{2}{3}\right)^2-\frac{2}{3}-2$
$=\frac{24}{9}-\frac{2}{3}-2 $
$ =\frac{8}{3}-\frac{2}{3}-2=0$
$ =8-8=0 $
$ =\text { R.H.S. }$
Hence, $x=\frac{2}{3}$ is a solution of given equation.

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