If $α$ and $β$ are the zero of the quadratic polynomial $p (x) = 4 x^{2} - 5 x - 1$ find value of $α^{2} β^{2} + α β^{2} .$

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Solution

If $α, β$ are the zeros of $p (x) = 4 x^{2} - 5 x - 1$
Then $α + β = \frac{5}{4}, α β = - \frac{1}{4}$
$α^{2} β + α β^{2} = (α β) (α + β) = - \frac{5}{16}$

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