$x^2 + bx + c = 0$
$x_1 = b$
$x_2 = c$
$\begin{equation*} \begin{cases} x_1 + x_2 = -b &\\ x_1x_2 = c & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} b + c = -b &\\ bc = c & \end{cases} \end{equation*}$
bc = c
bc − c = 0
c(b − 1) = 0
c = 0
или
b − 1 = 0
b = 1
Тогда:
$\begin{equation*} \begin{cases} 2b + c = 0 &\\ c = 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2b + 0 = 0 &\\ c = 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} b = 0 &\\ c = 0 & \end{cases} \end{equation*}$

$\begin{equation*} \begin{cases} 2b + c = 0 &\\ b = 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} c = -2b &\\ b = 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} c = -2 &\\ b = 1 & \end{cases} \end{equation*}$
Ответ: b = c = 0; b = 1 и c = −2.