[JEE Main 2014] if a in mathbb r and 3 x x 2 2 x x a
If $a\in\mathbb R$ and $-3(x-[x])^2+2(x-[x])+a^2=0$ (with $[x]$ the greatest integer $\le x$) has no integral solution, then all possible $a$ lie in
(a) $(-2,-1)$
(b) $(-\infty,-2)\cup(2,\infty)$
(c) $(-1,0)\cup(0,1)$
(d) $(1,2)$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 4d ago
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Correct answer: (c) $(-1,0)\cup(0,1)$
With $t=\{x\}\in[0,1)$, $a^2=3t^2-2t\in[0,1)$ requires $a\in(-1,1)$; excluding the integral solution $t=0$ (where $a=0$) gives $a\in(-1,0)\cup(0,1)$.
JEE Main 2014 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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