Školjka

%V0 Let $a,b,c$ be real numbers with $a$ non-zero. It is known that the real numbers $x_1,x_2,\ldots,x_n$ satisfy the $n$ equations:$$$\begin{align*} ax_1^2+bx_1+c &= x_{2} \\ ax_2^2+bx_2 +c &= x_3 \\ \vdots \\ ax_n^2+bx_n+c &= x_1 \end{align*}$$$ Prove that the system has zero, one or more than one real solutions if $(b-1)^2-4ac$ is negative, equal to zero or positive respectively.