If $α, β$ are zeroes of the polynomial $p (x) = {2 x}^{2} - 7 x + 3,$ find the value of $α^{3} β^{3}$

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Solution

$α, β$ are given of the polynomial $P (x) = 2 x^{2} - 7 x + 3$
where a=2, b = -7, c = 3.
now, $α β = \frac{c}{a}$
$\Rightarrow α β = \frac{3}{2}$
Hence $α^{3} β^{3} = (α β)^{3} = (\frac{3}{2})^{3} = \frac{27}{8} .$

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