Lời giải
Với a ≠ 0. Theo bài ra ta có:
\[\left\{ \begin{array}{l} - \frac{b}{{2a}} = 2\\\frac{{4ac - {b^2}}}{{4a}} = 4\\c = 6\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}b = - 4a\\24a - {b^2} = 16a\\c = 6\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}b = - 4a\\16{a^2} - 8a = 0\\c = 6\end{array} \right.\]
\[ \Leftrightarrow \left\{ \begin{array}{l}b = - 4a\\\left[ \begin{array}{l}a = 0\;\;\,\left( {KTM} \right)\\a = \frac{1}{2}\;\;\left( {TM} \right)\end{array} \right.\\c = 6\end{array} \right. \Rightarrow \left\{ \begin{array}{l}a = \frac{1}{2}\\b = - 2\\c = 6\end{array} \right.\].