If $α, β$ are the zeroes of the quadratic polynomial
$x^{2} + x - 2$ , then $(\frac{1}{α} - \frac{1}{β})^{2} =$

\frac{9}{4}

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\frac{- 9}{4}

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\frac{2}{5}

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\frac{- 2}{5}

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Solution

The correct option is A $\frac{9}{4}$
$α + β = - 1, α β = - 2$
$(\frac{1}{α} - \frac{1}{β})^{2} = (\frac{β - α}{α β})^{2} = \frac{(β + α)^{2} - 4 α β}{(α β)^{2}}$
$= \frac{(- 1)^{2} - 4 (- 2)}{4} = \frac{9}{4}$

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