If α, β are the roots of ax2+bx+c=0 ,then α2 + β2α-2+β-2 is

α+β=-ba, αβ=ca (α2+β2)1α2+1β2 =α2β2 =c2a2

If α, β are the roots of ax2+bx+c=0 ,then α2 + β2α-2+β-2 is

α+β=-ba, αβ=ca (α2+β2)1α2+1β2 =α2β2 =c2a2

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$I f α, β a r e t h e r o o t s o f a x^{2} + b x + c = 0, t h e n (\frac{α^{2} + β^{2}}{α^{- 2} + β^{- 2}}) i s$

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$\frac{c^{2}}{a^{2}}$

$\frac{(b^{2} - 2 a c)}{a c}$

$\frac{(3 a b c - b^{3})}{c^{3}}$

$\frac{(3 a b c - b^{3})}{a^{2} c}$

answer is A.

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Detailed Solution

$α + β = \frac{- b}{a}, α β = \frac{c}{a} \frac{(α^{2} + β^{2})}{(\frac{1}{α^{2}} + \frac{1}{β^{2}})} = α^{2} β^{2} = \frac{c^{2}}{a^{2}}$

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If α, β are the roots of ax2+bx+c=0 ,then α2 + β2α-2+β-2 is

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$I f α, β a r e t h e r o o t s o f a x^{2} + b x + c = 0, t h e n (\frac{α^{2} + β^{2}}{α^{- 2} + β^{- 2}}) i s$