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Quadratic Formula

If αand β...

Question

If $α$ and $β$ are the zeros of the quadratic polynomial $f (t) = t^{2} - 4 t + 3$ , find the value of $α^{4} β^{3} + α^{3} β^{4} .$

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Solution

$f (t) = t^{2} - 4 t + 3$
$α + β = 4$
$α β = 3$
$α^{4} β^{3} + α^{3} β^{4}$
$= α^{3} β^{3} (α + β)$
$= (3)^{3} \times 4$
$= 108$

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