Let be the set of all non-zero real numbers such that the quadratic equation has two…

MATHEMATICS · Multi correct · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Let SS be the set of all non-zero real numbers α\alpha such that the quadratic equation αx2−x+α=0\alpha x^2-x+\alpha=0 has two distinct real roots x1x_1 and x2x_2 satisfying ∣x1−x2∣<1|x_1-x_2|<1. Which of the following intervals are subsets of SS? (1) (−12,−15)\left(-\frac{1}{2},-\frac{1}{\sqrt{5}}\right) (2) (−15,0)\left(-\frac{1}{\sqrt{5}},0\right) (3) (0,15)\left(0,\frac{1}{\sqrt{5}}\right) (4) (15,12)\left(\frac{1}{\sqrt{5}},\frac{1}{2}\right)

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