JEE Main 2024MathematicsQuadratic EquationMediumNumerical

JEE Main 2024 — Quadratic Equation Question with Solution

JEE Main 2024 (30 Jan Shift 2)

Question

The number of real solutions of the equation is ______.

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Show full solutionCorrect answer: 1
Correct answer
1

Step-by-step explanation

Given,

xx2+3|x|+5|x-1|+6|x-2|=0

⇒x=0 or x2+3|x|+5|x-1|+6|x-2|=0

We know that sum of all positive terms can never be zero,

So, x2+3|x|+5|x-1|+6|x-2| can never be zero for any value of x,

So there is no value of x which satisfies the above equation
Hence, only solution is x=0, i.e. number of solution is 1 .

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About this question

This is a previous-year question from JEE Main 2024, 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.