$x^2+bx+c=0$
$x_1=b$
$x_2=c$
$\{\begin{array}{ll}{x}_1+x_2=-<!--\; -\; -->b& \\ x_1{x}_2=c& \end{array}$
$\{\begin{array}{ll}b+c=-<!--\; -\; -->b& \\ bc=c& \end{array}$
bc = c
bc − c = 0
c(b − 1) = 0
c = 0
или
b − 1 = 0
b = 1
Тогда:
$\{\begin{array}{ll}2b+c=0& \\ c=0& \end{array}$
$\{\begin{array}{ll}2b+0=0& \\ c=0& \end{array}$
$\{\begin{array}{ll}b=0& \\ c=0& \end{array}$

$\{\begin{array}{ll}2b+c=0& \\ b=1& \end{array}$
$\{\begin{array}{ll}c=-<!--\; -\; -->2b& \\ b=1& \end{array}$
$\{\begin{array}{ll}c=-<!--\; -\; -->2& \\ b=1& \end{array}$
Ответ: b = c = 0; b = 1 и c = −2.