If a ∈ 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:

Question

Accepted Answer

(−1, 0) ∪ (0, 1). The equation involves the term (x - [x]), which represents the fractional part of x. For the equation to have no integral solutions, the values of a must be such that the quadratic expression does not yield any real roots, which occurs when a is in the interval (-1, 0) ∪ (0, 1), ensuring that the discriminant is negative.

If a ∈ 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:

Solution

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