Determine whether the given values of variable is a solution of the quadratic equation or not. $7 x^{2} - 12 x = 0; x = \frac{1}{3}$

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Solution

The given quadratic equation is $7 x^{2} - 12 x = 0$ .

Substitute $x = \frac{1}{3}$ in the equation $7 x^{2} - 12 x = 0$ as follows:

$7 x^{2} - 12 x = 0 \Rightarrow 7 {(\frac{1}{3})}^{2} - (12 \times \frac{1}{3}) = 0 \Rightarrow (7 \times \frac{1}{9}) - 4 = 0 \Rightarrow \frac{7}{9} - 4 = 0 \Rightarrow \frac{7 - 36}{9} = 0 \Rightarrow - \frac{29}{9} = 0$
which is not true.

Hence, $x = \frac{1}{3}$ is not the solution of the quadratic equation $7 x^{2} - 12 x = 0$ .

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