If a R and the equation - 3(x - [ x ])² + 2(x - [ x ]) + a² = 0 (where [ x ] denotes the greater integer ≤ x) has no integral solution, then all possible values of a lie in the interval:

Complex Numbers and Quadratic Equations: JEE Main 2014 Mathematics question

JEE Main 2014 · Session, Shift 1 · Q5059

JEE Main 2014Session, Shift 1MathematicsHardComplex Numbers and Quadratic Equations264× since 2002

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 :