Relations Functions

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

  1. (-1, 0) U (0, 1)
  2. (-2, -1)
  3. (1, 2)
  4. (-∞, -2) U (2, ∞)

Solution

a2 = 3t2 - 2t

For non-integral solution

0 < a2 < 1

a ϵ (-1, 0) U (0, 1)

The correct option is A.