A) \[{{x}^{2}}+x+1=0\]
B) \[{{x}^{2}}-2x+2=0\]
C) \[{{x}^{2}}+2x+2=0\]
D) \[{{x}^{2}}+2x-2=0\]
E) none of these
Correct Answer: B
Solution :
If\[1+i\]is one root of equation, then another root will be\[1-i\]. \[\therefore \] Sum of roots\[=1+i+1-i=2\] and product of roots\[=(1+i)(1-i)=1-{{i}^{2}}\] \[=1+1=2\] \[\therefore \]Required equation will be \[{{x}^{2}}-\] (sum of roots) x + (product of roots) = 0 \[\Rightarrow \] \[{{x}^{2}}-2x+2=0\]
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