A) \[(-2,\text{ }4)\]
B) (1, 2)
C) \[(-\sqrt{2},\sqrt{2})\]
D) \[\left( -\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)\]
E) \[(-4,\text{ }2)\]
Correct Answer: D
Solution :
\[{{x}^{2}}+4ax+2>0\] \[\therefore \] \[{{(4a)}^{2}}-4{{x}^{2}}<0\] [\[\because \]if\[f(x)>0,\]then\[D<0\]] \[\Rightarrow \] \[16{{a}^{2}}<8\] \[\Rightarrow \] \[{{a}^{2}}<\frac{1}{2}\] \[\Rightarrow \] \[-\frac{1}{\sqrt{2}}<a<\frac{1}{\sqrt{2}}\]
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