JEE Advanced | 2015Quadratic EquationHard
Question
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 ?
Options
A.
B.
C.
D.
Solution
α x2 - x + α = 0
D = 1 - 4α2
distinct real roots D > 0
⇒ α ∈
...(i)
given |x1 - x2| < 1
⇒
< 1
⇒ 1 - 4α2 < α2
μ α ∈
...(ii)
from (i) & (ii)
α ∈
D = 1 - 4α2
distinct real roots D > 0
⇒ α ∈
...(i)given |x1 - x2| < 1
⇒
< 1⇒ 1 - 4α2 < α2
μ α ∈
...(ii)from (i) & (ii)
α ∈
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