If - and - are the roots of the equation x2 - 3x - 4 - 0- then 1- - 1- is equal to

The correct option is A 34 Given Quadratic Equation: x^2+3x 4=0 Sum of roots, #160; α+β= 3 andProduct of roots, #160; αβ= 4 1α+1β ...

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Standard XII

Mathematics

Algebra of Limits

If α and ...

Question

If $α$ and $β$ are the roots of the equation $x^{2} + 3 x - 4 = 0$ , then $\frac{1}{α} + \frac{1}{β}$ is equal to

\frac{- 3}{4}

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\frac{3}{4}

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\frac{- 4}{3}

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\frac{4}{3}

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\frac{3}{2}

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Solution

The correct option is A $\frac{3}{4}$
Given Quadratic Equation: $x^{2} + 3 x - 4 = 0$
Sum of roots, $α + β = - 3$ and
Product of roots, $α β = - 4$
$\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{- 3}{- 4} = \frac{3}{4}$
Hence, B is the correct option.

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If α and β are the roots of the equation x2+3x−4=0, then 1α+1β is equal to

The correct option is A 34Given Quadratic Equation: x2+3x−4=0Sum of roots, α+β=−3 andProduct of roots, αβ=−41α+1β=α+βαβ=−3−4=34Hence, B is the correct option.

If $α$ and $β$ are the roots of the equation $x^{2} + 3 x - 4 = 0$ , then $\frac{1}{α} + \frac{1}{β}$ is equal to

The correct option is A $\frac{3}{4}$
Given Quadratic Equation: $x^{2} + 3 x - 4 = 0$
Sum of roots, $α + β = - 3$ and
Product of roots, $α β = - 4$
$\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{- 3}{- 4} = \frac{3}{4}$
Hence, B is the correct option.