Đáp án: A
Giải thích các bước giải:
$\begin{array}{l}
F\left( x \right) = \left( {a{x^2} + bx - c} \right).{e^{2x}}\\
\Rightarrow F'\left( x \right) = \left( {2ax + b} \right).{e^{2x}} + 2.{e^{2x}}.\left( {a{x^2} + bx - c} \right)\\
\Rightarrow f\left( x \right) = \left( {2a{x^2} + 2bx - 2c + 2ax + b} \right).{e^{2x}}\\
\Rightarrow \left( {2018{x^2} - 3x + 1} \right).{e^{2x}} = \left( {2a{x^2} + \left( {2a + 2b} \right)x + b - 2c} \right).{e^{2x}}\\
\Rightarrow \left\{ \begin{array}{l}
2018 = 2a\\
- 3 = 2a + 2b\\
1 = b - 2c
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 1009\\
b = - \frac{{2021}}{2}\\
c = - \frac{{2023}}{4}
\end{array} \right. \Rightarrow T = - 3035
\end{array}$
