If α and β are the roots of the equation x 2 + p x + 2 = 0 and 1 α and 1 β are the roots of the equation 2 x 2 + 2 q x + 1 = 0 , then α - 1 α β - 1 β α + 1 β β + 1 α is equal to :

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α , β are roots of x 2 + p x + 2 = 0 ⇒ α + β = - p , α β = 2 1 α , 1 β are roots of 2 x 2 + 2 q x + 1 = 0 ∴ α , β are roots of x 2 + 2 q x + 2 = 0 ⇒ α + β = - 2 q , α β = 2 ∴ p = 2 q . . . ( i ) ⇒ α - 1 α β - 1 β α + 1 β β + 1 α = α β - α β - β α + 1 α β · α β + 1 α β + 2 ⇒ 2 - α + β 2 - 2 α β α β + 1 2 · 2 + 1 2 + 2 ⇒ 5 2 - p 2 - 4 2 · 9 2 = 9 4 9 - p 2 or, 9 4 9 - 4 q 2

Mathematics - Quadratic Equation Question with Solution | TestHub

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