1 Quadratic Equations
Let S be the set of all non-zero numbers a such that the quadratic equation αx2 – x + a = 0 has two distinct real roots x1 and x2 satisfying the inequality
|x1−x2|<1. Which of the following intervals is(are) a subset(s) of S ?
1) $$\left(-\frac{1}{2},-\frac{1}{\sqrt{5}}\right)$$
2) $$\left(-\frac{1}{\sqrt{5}}, 0\right)$$
3) $$\left(0, \frac{1}{\sqrt{5}}\right)$$
4) $$\left(\frac{1}{\sqrt{5}}, \frac{1}{2}\right)$$
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