JEE Main 2023MathematicsDeterminantsEasyMCQ

JEE Main 2023 — Determinants Question with Solution

JEE Main 2023 (11 Apr Shift 2)

Question

If x+1xxxx+λxxxx+λ2=98103x+81, then λ, λ3 are the roots of the equation
 

Choose an option

Show full solutionCorrect option: D
Correct answer
D4x2-24x+27=0

Step-by-step explanation

Given that, x+1xxxx+λxxxx+λ2=98103x+81

Put x=0 as x∈R

⇒1000λ000λ2=981030+81

On expanding the determinant we get,

⇒λ3=98×81

⇒λ3=9323

⇒λ=92 and λ3=96

Now the required quadratic equation is x2-92+96x+92×96=0

⇒x2-6x+274=0

⇒4x2-24x+27=0

Hence, the required quadratic equation is 4x2-24x+27=0

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About this question

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