Let $S$be the set of all non-zero real numbers such that the quadratic equation $\alpha x^2-x+\alpha =0$has two distinct real roots $x_{1}an{dx}_2$satisfying the inequality $\left|x_1-x_2\right|<1.$Which of the following intervals is (are) a subset (s) of $S?$$\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. $\left(\frac{1}{\sqrt{5}},\frac{1}{2}\right)$

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