JEE Main 2017MathematicsQuadratic EquationHardMCQ

JEE Main 2017 — Quadratic Equation Question with Solution

JEE Main 2017 (02 Apr)

Question

If, for a positive integer n, the quadratic equation,

xx+1+x+1x+2+...+x+n-1¯x+n=10n 

has two consecutive integral solutions, then n is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D11

Step-by-step explanation

On simplifying we get the quadratic equations as
x2+x2+...+x2⏟n times+1+3+5+...+2n-1x+1.2+2.3+...+n-1n=10n
nx2+n2x+nn2-13=10n

x2+nx+n2-313=0

Let, α, β are the roots of the above equation

∴ α+β=-n, αβ=n2-313

Now, the difference of roots α-β =1

⇒ α-β2=1

⇒α+β2-4αβ=1

⇒n2-43n2-31=1

⇒n2=121

⇒n=11

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About this question

This is a previous-year question from JEE Main 2017, 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.