JEE Main 2023MathematicsQuadratic EquationHardNumerical

JEE Main 2023 — Quadratic Equation Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

Let λ∈ℝ and let the equation E be |x|2-2|x|+|λ-3|=0. Then the largest element in the set S= {x+λ:x is an integer solution of E} is ______

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Given:

|x|2-2|x|+|λ-3|=0

⇒|λ-3|=x2-x

At λ=3, x=0 and 2,

At λ=4 or 2, then,

x=1 or -1

So, maximum value of x+λ=5 when x=1 and λ=4.

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About this question

This is a previous-year question from JEE Main 2023, 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.