Problem

Let

S

be the set of all non-zero real numbers

\alpha

such that the quadratic equation

\alpha x^2 - x + \alpha = 0

has two distinct real roots

x_1

and

x_2

satisfying the inequality

|x_1 - x_2| < 1

. Which of the following intervals is (are) a subset(s) of

S

? a.

\left(-\frac{1}{2}, -\frac{1}{\sqrt{5}}\right)

\left(-\frac{1}{\sqrt{5}}, 0\right)

\left(0, \frac{1}{\sqrt{5}}\right)

\left(\frac{1}{\sqrt{5}}, \frac{1}{2}\right)