A) \[f(x)>0\] for all x
B) \[f(x)>1\] when \[x\ge 0\]
C) \[f(x)\ge 1\] when \[x\le -4\]
D) \[f(x)=f(-x)\] for all \[x\]
Correct Answer: C
Solution :
Since f (x) is a quadratic expression having real roots. Therefore f (x) does not have the same sign for all x. \[f(x)\ge 1\Rightarrow {{x}^{2}}+4x+1\ge 1\,\Rightarrow {{x}^{2}}+4x\ge 0\] Þ \[x\le -4\]or \[x\ge 0\].
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