Question

determine whether x=1/2 ,x=1/3, are the solution of the given equation 6x2 - x-2 =0 ,or not$give answer?

Answer 1

We need to substitute the values of $x$ in given equation

             $6x^{2} -x-2=0$  and check whether we get RHS as $0$

Given:    $6x^{2} -x-2=0$

      We substitute $x=\frac{1}{2}$ in LHS of the given equation

                                  $6(\frac{1}{2})^{2}-\frac{1}{2}-2\\ =\frac{3}{2} -\frac{1}{2} -2$
                                  $=1-2\\=-1$

Thus we don't get $x=\frac{1}{2}$ as a solution.

Now we substitute $x=\frac{1}{3}$ in LHS of the given equation,

                                  $6(\frac{1}{3} )^{2} -\frac{1}{3} -2\\=-\frac{5}{3}$

                   Hence, $x=\frac{1}{2},$

                                $x=\frac{1}{3}$ are not solutions of the given equation