Ans: A
$\begin{array}{rcl}
x(x+3a)+a & \equiv & x^2 + 2(bx+c) \\
x^2 +3ax + a & \equiv & x^2 +2bx +2c
\end{array}$
$\begin{array}{rcl}
x(x+3a)+a & \equiv & x^2 + 2(bx+c) \\
x^2 +3ax + a & \equiv & x^2 +2bx +2c
\end{array}$
By comparing the coefficients of both sides, we have
$\left\{ \begin{array}{ll}
3a=2b & \ldots \unicode{x2460} \\
a=2c & \ldots\unicode{x2461}
\end{array}\right.$
From $\unicode{x2460}$, we have
$\begin{array}{rcl}
3a & = & 2b \\
\dfrac{a}{b} & = & \dfrac{2}{3} \\
a:b & = & 2: 3
\end{array}$
From $\unicode{x2461}$, we have
$\begin{array}{rcl}
a & = & 2c \\
\dfrac{a}{c} & = & 2 \\
a:c & = & 2:1
\end{array}$
Therefore, we have $a:b:c =2:3:1$.
