A) \[(-1,-4)\]
B) \[(\pm 1,\pm 4)\]
C) \[(-4,4)\]
D) None of these
Correct Answer: D
Solution :
Given, equation is \[{{x}^{2}}+5|x|+4=0\] If\[x>0,\]then\[|x|=x\] \[\therefore \] \[{{x}^{2}}+5x+4=0\] \[\Rightarrow \] \[{{x}^{2}}+4x+x+4=0\] \[\Rightarrow \] \[(x+4)(x+1)=0\] \[\Rightarrow \] \[x=-4,-1\] If\[x<0,\]then\[|x|=-x\] \[\therefore \] \[{{x}^{2}}-5x+4=0\] \[\Rightarrow \] \[{{x}^{2}}-4x-x+4=0\] \[\Rightarrow \] \[(x-4)(x-1)=0\] \[\Rightarrow \] \[x=4,1\] Hence, no real roots exist.
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