JEE Math Practice Question

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

1. A.$$\left( { - 2, - 1} \right)$$
2. B.$$\left( { - \infty , - 2} \right) \cup \left( {2,\infty } \right)$$
3. C.$$\left( { - 1,0} \right) \cup \left( {0,1} \right)$$
4. D.$$\left( {1,2} \right)$$