Question

If one root of the quadratic equation $6x^2-x-k=0$ is $\frac{2}{3}$, then find the value of $k$.

Answer 1

Let $f\left(x\right)=6x^2-x-k$ as $\frac{2}{3}$ is a root

$\Rightarrow f\left(\frac{2}{3}\right)=0$

$\Rightarrow 6\left(\frac{4}{9}\right)-\frac{2}{3}-k=0$

$\Rightarrow \frac{8}{3}-\frac{2}{3}=k$

$\Rightarrow k=2$.