Let S be the set of all non-zero real numbers $$\alpha$$ such that the quadratic equation $$ax^2 - x + a = 0$$ 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

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

B

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

C

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

D

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