If \[a\in R\] 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 of a lie iin the interval:
A)\[(-1,0)\cup \,(0,1)\]
B)(1, 2)
C)\[(-2,-\,1)\]
D)\[(-\infty ,-\,2)\cup \,(2,\infty )\]
Correct Answer:
A
Solution :
\[{{a}^{2}}=3{{t}^{2}}-2t\] For non-integral solution \[0<{{a}^{2}}<1\] \[a\in (-1,0)\cup (0,1).\]