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If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x) = x^2 – (k + 5)x + (5k + 1)$ such that, $\alpha + \beta = \frac{\alpha\beta}{3}$, then find the value of k.
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Here, $\alpha + \beta = (k + 5)$ and $\alpha\beta = (5k + 1)$
Given, $\alpha + \beta = \frac{\alpha\beta}{3}$
$k+5 = \frac{5k+1}{3}$
$\Rightarrow k = 7$
Given, $\alpha + \beta = \frac{\alpha\beta}{3}$
$k+5 = \frac{5k+1}{3}$
$\Rightarrow k = 7$