Question

If one root of the quadratic equation 6x² – x – k = 0 is

\[\frac{2}{3},\] then find the value of k.

Answer 1

The given quadratic equation is 6x² − x − k = 0.
Since 2323 is one root of the given quadratic equation, so

\[6 \left( \frac{2}{3} \right)^2 - \frac{2}{3} - k = 0\]
\[ \Rightarrow 6 \times \frac{4}{9} - \frac{2}{3} - k = 0\]
\[ \Rightarrow k = \frac{8}{3} - \frac{2}{3} = \frac{6}{3} = 2\]

Thus, the value of k is 2.