JEE Main 2014MathematicsQuadratic EquationHardMCQ

JEE Main 2014 — Quadratic Equation Question with Solution

JEE Main 2014 (06 Apr)

Question

If a ∈ R  and the equation -3(x - [x])2+2(x - [x])+a2 = 0 (where [x] denotes the greatest integer ≤  x) has no integral solution, then all possible values of a lie in the interval 

Choose an option

Show full solutionCorrect option: C
Correct answer
C - 1 ,  0 ∪ 0 ,  1

Step-by-step explanation

Let    x-[x]=t

∴   -3t2+2t+a2=0

As x is not an integer, t≠0     ∴  a≠0

For a root of x to exist at least one of the roots of t should be between 0 and 1.

Roots    =-2±4-4-3a2-6

              =-2±4+12a2-6

              =-1±1+3a2-3=1∓1+3a23

As we observe, one root is surely less than zero,

i.e.,   1-1+3a23

∴    For a solution to exist,

       1+1+3a23<1

∴   1+1+3a2<3

∴   1+3a2<2

∴   1+3a2<4

∴   3a2<3

∴   a2<1

∴   a∈-1,0∪0,1.     ∵   a≠0

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About this question

This is a previous-year question from JEE Main 2014, 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.