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Question

Solution of inequality (x−1)2(x+1)3(x−4)<0 is

A
1<x<3
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B
2<x<4
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C
1<x<4
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D
1<x<2
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Solution

The correct option is C 1<x<4
Given, (x1)2(x+1)3(x4)<0
Since square of a number cannot be <0
This means, one of (x+1)3 or (x4) is <0
Now, (x+1)3<0 and x4>0 => x<1 and x>4 --- (1)
OR (x+1)3>0 and x4<0 => x>1 and x<4 --- (2)
From solutions of both possibilities, 1<x<4

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