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Question

The largest interval among the following for which x12x9+x4x+1>0 is

A
4<x0
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B
0<x<1
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C
100<x<100
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D
<x<
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Solution

The correct option is D <x<

If x0, then x12x9+x4x+1>0


If 0<x1, then x12+x4(1x5)+(1x)>0


If x>1, then x9(x31)+x(x31)+1>0


So the expression x12x9+x4x+1>0 is valid for <x<


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