JEE Main 2019MathematicsQuadratic EquationMediumMCQ

JEE Main 2019 — Quadratic Equation Question with Solution

JEE Main 2019 (12 Apr Shift 2)

Question

If α,β and γ are three consecutive terms of a non-constant G.P. Such that the equations αx2+2βx+γ=0 and x2+x-1=0 have a common root, then αβ+γ is equal to:

Choose an option

Show full solutionCorrect option: A
Correct answer
Aβγ

Step-by-step explanation

Given α, β,γ are in G.P.⇒β2=αγ
For the equation αx2+2βx+γ=0
D=4β2-4αγ=0
Hence roots of the equation are equal and equals to –βα=-γβ
Since given equation have common roots, hence -γβ must be a root of x2+x-1=0
⇒ γ2β2-γβ-1=0
⇒ γ2-γ β-β2=0
⇒ γ2=ββ+γ
⇒ γ.β2α=ββ+γ
⇒ αβ+γ=βγ

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About this question

This is a previous-year question from JEE Main 2019, covering the Quadratic Equation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.