If $α a n d β$ ( $α < β$ ) are the roots of equation $x^{2} + 2 x - 5 = 0$ , then the value of $\frac{1}{α} - \frac{1}{β}$ is:

\frac{- 2 \sqrt{6}}{5}

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\frac{- \sqrt{24}}{5}

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\frac{2 \sqrt{6}}{5}

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\frac{\sqrt{24}}{5}

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Solution

The correct options are
A $\frac{- 2 \sqrt{6}}{5}$
B $\frac{- \sqrt{24}}{5}$
On comaring given equation with $a x^{2} + b x + c = 0$ we get a=1, b=2, c=-5
Let the roots be $α$ and $β$ .
$∴ α + β = \frac{- b}{a} = \frac{- 2}{1} = - 2 a n d α β = \frac{c}{a} = \frac{- 5}{1} = - 5 N o w, \frac{1}{α} - \frac{1}{β} = \frac{β - α}{α β} = \frac{\sqrt{(α + β)^{2} - 4 α β}}{α β} = \frac{\sqrt{(- 2)^{2} - 4 (- 5)}}{- 5} = \frac{- \sqrt{24}}{5} = \frac{- 2 \sqrt{6}}{5}$

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If α and β (α < β ) are the roots of equation x2+2x−5=0, then the value of 1α−1β is:

The correct options are A −2√65 B −√245On comaring given equation with ax2+bx+c=0 we get a=1, b=2, c=-5 Let the roots be α and β. ∴α+β=−ba=−21=−2 andαβ=ca=−51=−5Now, 1α−1β=β−ααβ=√(α+β)2−4αβαβ=√(−2)2−4(−5)−5=−√245=−2√65

If $α a n d β$ ( $α < β$ ) are the roots of equation $x^{2} + 2 x - 5 = 0$ , then the value of $\frac{1}{α} - \frac{1}{β}$ is: