Let a ∈ ℝ and let f : ℝ → ℝ be given by f(x) = x^5 - 5x + a. Then

JEE Advanced 2014 Mathematics question

Mathematics Application of Derivatives JEE Advanced 2014

Let a ∈ ℝ and let f : ℝ → ℝ be given by

f(x) = - 5x + a.

Then

(A)f(x) has three real roots if a > 4
(B)f(x) has only one real root if a > 4Correct
(C)f(x) has three real roots if a < −4
(D)f(x) has three real roots if −4 < a < 4Correct

Answer: (B),(D)

Solution

at x = ±1. f has a local maximum and a local minimum , and as . Three real roots occur when the local max is positive and the local min is negative: $-4

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Question ID VK-026287