## Task 16/76

Given the equation $x^{3}-4 x^{2}-17 x+a_{0}=0$, it is known that the sum of two of its solutions is 1. The goal is to find $a_{0}$.
According to Vieta's formula, $x_{1}+x_{2}+x_{3}=4$, where the $x_{i}$ are the solutions of the equation. W.L.O.G., let $x_{1}+x_{2}=1$. Then it follows that $x_{3}=3$. Substituting this value into the given equation, we obtain

$$
27-4 \cdot 9-17 \cdot 3+a_{0}=0
$$

and thus immediately $a_{0}=60$.