Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$. Let $\alpha ,\beta $ be roots of quadratic equation. If there are at least four negative integers between $\alpha$ and $\beta$, then the complete set of values of $a$ is

Substituting x = 1 into the quadratic equation gives a + 2 - a - 2 = 0, meaning one root is always 1. Since the product of the roots is -2/a, the other root must be -2/a. For there to be at least four negative integers (which must be -1, -2, -3, and -4) between the roots, the second root must be strictly less than -4, which simplifies to 0 < a < 1/2.