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

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Senior Manager
Joined: 17 Mar 2014
Posts: 375
What is the range of x such that x^7 - x^5 < 0 ?  [#permalink]

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14 Aug 2018, 17:15
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:41) correct 43% (01:15) wrong based on 35 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. $$0<x<1$$
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 936
WE: Supply Chain Management (Energy and Utilities)
What is the range of x such that x^7 - x^5 < 0 ?  [#permalink]

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15 Aug 2018, 07:04
1
1
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 ? &nbs [#permalink] 15 Aug 2018, 07:04
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# What is the range of x such that x^7 - x^5 < 0 ?

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