# The Line Rotates Again

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

All-Russian School Olympiad in Informatics 2025–2026, Final Stage<br>
“Artificial Intelligence” profile, Tour 1, Moscow, 23 March 2026<br>
Task A

Consider a linear classifier on the plane $\mathbb{R}^2$ defined by the line $x + Ay = 0$. A point $(x, y)$ belongs to the first class if $x + Ay > 0$. Otherwise, if $x + Ay \leq 0$, the point belongs to the second class.

Give an example of **integers** $A$, $b$ and $c$ such that, for the trinomial $P(x) = x^2 + bx + c$, the point $(2, P(2))$ belongs to the first class, while the points $(1, P(1))$ and $(3, P(3))$ belong to the second class.