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What is the range of x such that x^7 - x^5 < 0 ?

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What is the range of x such that x^7 - x^5 < 0 ?  [#permalink]

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New post 14 Aug 2018, 18:15
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Difficulty:

  45% (medium)

Question Stats:

59% (01:54) correct 41% (01:31) wrong based on 49 sessions

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What is the range of x such that x^7 - x^5 < 0 ?

A. \(x<-1\)
B. \(-1<x<1\)
C. \(x<-1, 0<x<1\)
D. \(-1<x<0, 1<x\)
E. \(0<x<1\)
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What is the range of x such that x^7 - x^5 < 0 ?  [#permalink]

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New post 15 Aug 2018, 08:04
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ammuseeru wrote:
What is the range of x such that x^7 - x^5 < 0 ?

A. \(x<-1\)
B. \(-1<x<1\)
C. \(x<-1, 0<x<1\)
D. \(-1<x<0, 1<x\)
E. \(0<x<1\)


Given, \(x^7-x^5<0\)
Or, \(x^5(x^2-1)<0\)
Or, \(x^5(x+1)(x-1)<0\)

Using wavy curve method to find the interval of 'x':-

a) Let f(x)= \(x^5(x+1)(x-1)<0\)
Finding out the critical points of f(x)=0, we have x=0,-1,1

b) Arranging the critical points in ascending order: -1,0,1

c) We observed that all the indices of the critical points are odd. (When the power of is odd number cross the number-line otherwise repeat in the same direction)

d) Let' draw the diagram. (Enclosed for reference)

e) We have to consider those set of values which are below the number line as the inequality sign is <.

So, \(x: \:\left(-\infty \:,\:-1\right)\cup \left(0,\:1\right)\)

Ans. (C)
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What is the range of x such that x^7 - x^5 < 0 ?   [#permalink] 15 Aug 2018, 08:04
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