From the meaning of the question, u(x) is a decreasing function on (-∞,-1/2), and it is always positive.

∴a/2≥- 1/2, and u (-1/2) = (1/4)-(a/2) ≥ 0,

That is, a≥-1 and a≤ 1/2,

The range of ∴a is-1≤a≤ 1/2.