Find the value of $p$ , if $x = 6$ is a root of the quadratic equation $3 x^{2} - p x - 24 = 0$ .

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Solution

Since, $x = 6$ is a root of $3 x^{2} - p x - 24 = 0$

$\begin{matrix} \Rightarrow 3 (6)^{2} - p \times 6 - 24 & = 0 \Rightarrow 108 - 6 p - 24 & = 0 \Rightarrow 6 p & = 84 \Rightarrow p & = 14 \end{matrix}$

Hence, $p = 14$ .

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