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Mathematics · 2014
JEE Main 2014 · 2014-04-06 Offline · Q63
If a ε R and the equation -3(x-[x])^2+2(x-[x])+ a^2=0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values…
If $\displaystyle \mathrm{a} \boldsymbol{\epsilon} \mathbf{R}$ and the equation
$$-3(x-[x])^2+2(x-[x])+\mathrm{a}^2=0
$$
(where $\displaystyle [x]$ denotes the greatest integer $\displaystyle \leq x)$ has no integral solution, then all possible values of a lie in the interval :
Official answer
(3)
$\displaystyle (-1,0) \cup(0,1)$
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JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.