If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x) = kx^2 - 30x + 45k$ and $\alpha + \beta = \alpha\beta$, then the value of $k$ is:

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Step 1: $\alpha + \beta = \frac{30}{k}$, $\alpha\beta = \frac{45k}{k} = 45$. Given $\alpha + \beta = \alpha\beta \Rightarrow \frac{30}{k} = 45 \Rightarrow k = \frac{2}{3}$

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