KöMaL 2025 B5432

Is it possible to find real numbers $a$, $b$ and $c$ such that none of the functions below has a root? $$\begin{gather*} p_1(x)=ax^2-(b^2+1)x+c,\\ p_2(x)=bx^2-(c^2+1)x+a,\\ p_3(x)=cx^2-(a^2+1)x+b. \end{gather*}$$