\(x=\left\{1,2\right\}\) là nghiệm \(\Rightarrow\left\{{}\begin{matrix}f\left(1\right)=0\\f\left(2\right)=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}1^2+b.1+c=0\\2^2+b.2+c=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}b+c+1=0\\2b+c+4=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}b=-3\\c=2\end{matrix}\right.\)