question_answer

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 \[0<{{a}^{2}}<1\] \[a\in (-1,0)\cup (0,1).\]