1. The parabola $y=x^{2}-20 x+c$, where $c \neq 0$, intersects the $O x$ axis at points $A$ and $B$, and the $O y$ axis at point $C$. It is known that points $A$ and $C$ are symmetric with respect to the line $y=-x$. Find the area of triangle $A B C$.
Answer: 231.

Solution. Since $y(0)=c$, we have $C(0, c)$ and $A(-c, 0)$. Therefore, one of the roots of the equation $x^{2}-20 x+c=0$ is $-c$, i.e., $c^{2}+20 c+c=0$, from which $c=-21, x_{1}=21$. By Vieta's theorem, $x_{1}+x_{2}=20$. Thus, $x_{2}=-1$. The length of the base of the triangle is $x_{1}-x_{2}=22$, and the height is 21.

Evaluation. 7 points for a correct solution.