question_answer

If \[\underset{x\to 1}{\mathop{\lim }}\,\frac{a{{x}^{2}}+bx+c}{{{(x-1)}^{2}}}=2\] then which of the following relation is correct?

A)  \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=12\]  

B)  \[a+c=b\]

C)  \[{{a}^{2}}+{{c}^{2}}=2b\]           

D)  \[{{b}^{2}}=2({{a}^{2}}+{{c}^{2}})\]