Question

If $x=\frac{2}{3}$ is a solution of the quadratic equation $7x^2+mx-3=0$, find the value of m.

• A. $m=\frac{1}{6}$.
• B. $m=\frac{-1}{3}$.
• C. $m=\frac{-1}{6}$.
• D. $m=\frac{1}{3}$.

Answer 1

The correct option is C

$m=\frac{-1}{6}$.

Given: $x=\frac{2}{3}$ is a solution of the quadratic equation $7x^2+mx-3=0$.

Substituting $x=\frac{2}{3}$ in the given quadratic equation we get

$\Rightarrow$ $7(\frac{2}{3}{)}^2+m(\frac{2}{3})-3=0$

$\Rightarrow$ $7\left(\frac{4}{9}\right)+m\left(\frac{2}{3}\right)-3=0$

$\Rightarrow$ $\frac{28}{9}+\frac{2m}{3}-3=0$

$\Rightarrow$ $28+6m-27=0$

$\Rightarrow$ $m=\frac{-1}{6}$