# JEE-Advanced 2015 (29/40)

Algebra Level 3

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.

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