# JEE-Advanced 2015 (29/40)

**Algebra**Level 4

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 of \(S\)?

\[\begin{array}{} (1) \, \left( -\frac{1}{2}, -\frac{1}{\sqrt5} \right) \quad \quad \quad \quad & (2) \, \left( -\frac{1}{\sqrt5},0 \right) \\ (3) \, \left( 0, \frac{1}{\sqrt5} \right) & (4) \, \left( \frac{1}{\sqrt5}, \frac{1}{2} \right) \end{array}\]

**Note :**

Submit your answer as the increasing order of the serial numbers of all the correct options.

For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.