If , and are three consecutive terms of a non-constant G .P . such that the equations x^2+2 βx+ =0 and x^2+x-1=0have a common root, then ( + ) is equal to:

Question

Accepted Answer

Correct answer: D. (d) JEE Main 2019 ∵ , , are three consecutive terms of a non-constant G .P . ∴ ^2= αγ So roots of the equation x^2+2 βx+ =0 are -2 2 ^2- αγ2 = ∵ x^2+2 βx+ =0 and x^2+x-1=0 have a common root. ∴ this root satisfy the equation x^2+x-1=0 ^2- αβ- ^2=0 ⇒ αγ- αβ- ^2=0 ⇒ + = Now, ( + )= αβ+ αγ = αβ+ ^2= ( + ) = βγ

$If α, β and γ are three consecutive terms of a non-constant G . P . such that the equations α x^{2} + 2 βx + γ = 0 and x^{2} + x - 1 = 0 have a common root, then α (β + γ) is equal to:$

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