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Definition of Functions

If α and ...

Question

If $α$ and $β$ are the zeroes of the polynomial $x^{2} - 5 x + 6$ then find the value of $\frac{1}{α^{2}} + \frac{1}{β^{2}}$

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Solution

$x^{2} - 5 x + 6$
$x^{2} - 2 x - 3 x + 6$
$x (x - 2) - 3 (x - 2)$
$(x - 2) (x - 3) α, β = 2, 3$
$\frac{1}{α^{2}} + \frac{1}{β^{2}} = \frac{1}{4} + \frac{1}{9}$
$= \frac{13}{36}$

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