Complex Numbers And Quadratic Equations question 26
Question: Let $ f(x)=x^{2}+4x+1 $ . Then
Options:
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 $
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Answer:
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 $ .
BETA
