[JEE Advanced 2015] let s be the set of non zero real alpha such that alpha x
Let $S$ be the set of non-zero real $\alpha$ such that $\alpha x^2-x+\alpha=0$ has two distinct real roots $x_1,x_2$ with $|x_1-x_2|<1$. Which intervals are subsets of $S$?
(a) $\left(-\frac12,-\frac1{\sqrt5}\right)$
(b) $\left(-\frac1{\sqrt5},0\right)$
(c) $\left(0,\frac1{\sqrt5}\right)$
(d) $\left(\frac1{\sqrt5},\frac12\right)$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (a) $\left(-\frac12,-\frac1{\sqrt5}\right)$
Distinct real roots need $|\alpha|<\frac12$; $|x_1-x_2|=\frac{\sqrt{1-4\alpha^2}}{|\alpha|}<1\Rightarrow|\alpha|>\frac1{\sqrt5}$. So $\frac1{\sqrt5}<|\alpha|<\frac12$ — intervals (a) and (d).
JEE Advanced 2015 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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