JEE Main 2019MathematicsQuadratic EquationEasyMCQ

JEE Main 2019 — Quadratic Equation Question with Solution

JEE Main 2019 (10 Jan Shift 2)

Question

The value of λ such that sum of the squares of the roots of the quadratic equation, x2+3-λ x+2=λ has the least value is:

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Show full solutionCorrect option: A
Correct answer
A2

Step-by-step explanation

We have, x2+(3-λ)x+2=λ, have roots α & β.

Then, f(λ)=α2+β2

=α+β2-2αβ=3-λ2-22-λ=λ2-6λ+9-4+2λ=λ2-4λ+5

f′λ=2λ-4=0 { for the minimum value of fλ}

As f''(λ)=2>0

⇒λ=2

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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.