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 of a lie in the interval

- (-1, 0) U (0, 1)
- (-2, -1)
- (1, 2)
- (-∞, -2) U (2, ∞)

**Solution**

a^{2} = 3t^{2} - 2t

For non-integral solution

0 < a^{2} < 1

a ϵ (-1, 0) U (0, 1)

**The correct option is A.**