Chapter 21: Problem 49
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 \(\left|x_{1}-x_{2}\right|<1\). Which of the following intervals is(are) a subset(s) of \(S\) ? (A) \(\left(-\frac{1}{2},-\frac{1}{\sqrt{5}}\right)\) (B) \(\left(-\frac{1}{\sqrt{5}}, 0\right)\) (C) \(\left(0, \frac{1}{\sqrt{5}}\right)\) (D) \(\left(\frac{1}{\sqrt{5}}, \frac{1}{2}\right)\)
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.