JEE Main 2022MathematicsQuadratic EquationMediumMCQ

JEE Main 2022 — Quadratic Equation Question with Solution

JEE Main 2022 (26 Jul Shift 2)

Question

The minimum value of the sum of the squares of the roots of x2+3-ax=2a-1 is

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Show full solutionCorrect option: A
Correct answer
A6

Step-by-step explanation

Let α,β be the roots of the equation

x2+3-ax+1-2a=0

Then, sum of roots α+β=a-3

And product of roots αβ=1-2a

We know that α2+β2=α+β2-2αβ

∴α2+β2=a-32-21-2a

=a2-2a+7

=a-12+6

∴ Minimum value of α2+β2=6 at a=1.

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About this question

This is a previous-year question from JEE Main 2022, 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.