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$\alpha, \beta$ are zeroes of the polynomial $3x^2 - 8x + k$. Find the value of $k$, if $\alpha^2 + \beta^2 = \frac{40}{9}$.
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$p(x) = 3x^2 - 8x + k \Rightarrow \alpha + \beta = \frac{8}{3}, \alpha\beta = \frac{k}{3}$
$\alpha^2 + \beta^2 = \frac{40}{9} \Rightarrow (\frac{8}{3})^2 - \frac{2k}{3} = \frac{40}{9} \Rightarrow k = 4$
$\alpha^2 + \beta^2 = \frac{40}{9} \Rightarrow (\frac{8}{3})^2 - \frac{2k}{3} = \frac{40}{9} \Rightarrow k = 4$