A) \[-\frac{4}{3}<a<\frac{4}{3}\]
B) \[-\frac{2}{3}<a<\frac{2}{3}\]
C) \[a\in \]null set
D) \[0<a<\frac{7}{3}\]
Correct Answer: B
Solution :
(b): Since the coefficient of \[{{x}^{2}}\] is 1 which is positive, therefore the given expression is positive for all real values of x if D < 0, therefore the given expression is positive for all real values of x if D<0. \[\Rightarrow {{\left( -a \right)}^{2}}-4\left( 1-2{{a}^{2}} \right)<0\] \[\Rightarrow 9{{a}^{2}}-4<0\] \[\Rightarrow \left( 3a+2 \right)\left( 3a-2 \right)<0\] \[\Rightarrow -\frac{2}{3}<a<\frac{2}{3}\]
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