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

Options

A. `(-1,0) cup (0,1)`
B. `(1,2)`
C. `(-2,-1)`
D. `(-oo,-2)cup (2,oo)`

Answer

A

Explanation

`a^(2)=3t^(2)-2t, " where " t={x} in [0,1)`
` :. a^(2) =3t(t-2//3)`
Graph of `f(t)=3t(t-2//3)` is as shown in the following figure.

Clearly, from graph
`0 lt a^(2) lt 1`
`or a in (-1,0) cup (0,1) `