A) \[0<x<1\]
B) \[-4<x\le 0\]
C) \[0<x<\infty \]
D) \[-10<x<10\]
Correct Answer: C
Solution :
Given, \[{{x}^{12}}-{{x}^{9}}+{{x}^{4}}-x+1>0\] If \[x\le 0,\]then \[{{x}^{12}}-{{x}^{9}}+{{x}^{4}}-x+1>0\] If \[0<x<1,\]then \[{{x}^{12}}-{{x}^{9}}+{{x}^{4}}-x+1\] \[={{x}^{12}}+{{x}^{4}}(1-{{x}^{5}})-x+1>0\] If \[x\ge 1,\]then \[{{x}^{12}}-{{x}^{9}}+{{x}^{4}}-x+1>0\] Hence, the greatest interval is\[0<x<\infty \].
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