Question

If alpha and beta are the zeroes of x²-px+q then
$\frac{1}{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} } =$
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Answer 1

$=> \alpha + \beta = \frac{ - b}{a}$

$= \frac{p}{1} = p$

$= \alpha p = \frac{q}{1} = q$

$\frac{1}{ \alpha^{2} } + \frac{1}{ { \beta }^{2} } = \frac{ { \beta }^{2} + { \alpha }^{2} }{ { \alpha }^{2} { \beta }^{2} }$

$= \frac{( \alpha + { \beta )}^{2} - 2 \alpha \beta }{( { \alpha \beta }^{2} )}$

$= \frac{ {p}^{2} - 2q }{ {q}^{2} }$