JEE Main 2020MathematicsQuadratic EquationMediumMCQ

JEE Main 2020 — Quadratic Equation Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

Let α and β be the roots of x2-3x+p=0 and γ and δ be the roots of x2-6x+q=0. If α,β,γ,δ from a geometric progression. Then ratio (2 q+p):(2 q-p) is

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Show full solutionCorrect option: B
Correct answer
B9:7

Step-by-step explanation

Let α=a, β=ar, γ=ar2, δ=ar3

α+β=3  ⇒a+ar=3  ...........1

γ+δ=6 ⇒ar2+ar3=6   .........2

By 1 and 2 ⇒ ar21+ra1+r=63

⇒ r2=2

∴  2q+p2q−p=2γδ+αβ2γδ−αβ=2a2r5+a2r2a2r5−a2r=2r4+12r4−1=8+18−1=97

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About this question

This is a previous-year question from JEE Main 2020, 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.