If a ϵ R and the equation -3(x - [x])^2 + 2(x - [x]) + a^2 = 0 has no integral solution

• 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.