A) \[\left( -\frac{1}{2},0 \right)\]
B) \[(-\infty ,-2)\cup (2,\infty )\]
C) \[\left( -\frac{1}{2},0 \right)\cup \left( 0,\frac{1}{2} \right)\]
D) \[\left( 0,\frac{1}{2} \right)\]
Correct Answer: C
Solution :
\[(a-1)\left( {{x}^{2}}+x+1 \right)\left( {{x}^{2}}-x+1 \right)+(a+1){{\left( {{x}^{2}}+x+1 \right)}^{2}}=0\] \[\Rightarrow \]\[{{x}^{2}}+x+1\]or\[(a-1)\left( {{x}^{2}}-x+1 \right)+(a+1)\left( {{x}^{2}}+x+1 \right)=0\] \[\Rightarrow \]\[a{{x}^{2}}+x+a=0\] For real & unequal roots D > 0 \[\Rightarrow \]\[1-4{{a}^{2}}>0\] \[\Rightarrow \]\[a\in \left( -\frac{1}{2},\frac{1}{2} \right)-\left\{ 0 \right\}\]\[\because \]\[a\ne 0\]
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