Question

If one root of the quadratic equation 3y² – ky + 8 = 0 is $\frac{2}{3}$ then find the value of k.

Answer 1

Given: y = $\frac{2}{3}$ is the root of the quadratic equation 3y² – ky + 8 = 0.

Thus, y = $\frac{2}{3}$ satisfies the given equation.

Therefore,

$$\begin{gathered} 3{\left(\frac{2}{3}\right)}^2-k\left(\frac{2}{3}\right)+8=0 \\ \Rightarrow 3\times \frac{4}{9}-\frac{2k}{3}+8=0 \\ \Rightarrow \frac{4}{3}-\frac{2k}{3}+8=0 \\ \Rightarrow \frac{4-2k+24}{3}=0 \end{gathered}$$

On multiplying both sides by 3, we get:
4 – 2k + 24 = 0

$\Rightarrow$–2k + 28 = 0

$\Rightarrow$–2k = –28

$\Rightarrow$k = $\frac{-28}{-2}=14$