Question

If $y=\frac{2}{3}$ is a root of the quadratic equation $3y^2-ky+8=0$, then the value of $k$ is ..................

• A. $13$
• B. $-14$
• C. $14$
• D. $-13$

Answer 1

The correct option is C $14$

$y$ is the root of given quadratic equation. So, it satisfy the quadratic equation $3y^2-ky+8=0$

$\therefore$ substitute $y=\frac{2}{3}$ in $3y^2-ky+8=0$

$\Rightarrow 3{\left(\frac{2}{3}\right)}^2-k\left(\frac{2}{3}\right)+8=0$

$\Rightarrow 3\times \frac{4}{9}-\frac{2k}{3}+8=0$

$\Rightarrow \frac{4}{3}+8=\frac{2k}{3}\Rightarrow k=14$

Hence, the answer is $14$.