\[\boxed{\text{787.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[x^{2} + px + q = (x - p)(x - q)\]
\[(x - p)(x - q) = x^{2} - qx -\]
\[- px + qp = x^{2} - (p + q)x + pq.\]
\[По\ теореме\ Виета:\]
\[\left\{ \begin{matrix} pq = q\ \ \ \ \ \ \ \ \ \ \\ - (p + q) = p \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} p = 1\ \ \ \ \ \ \ \ \ \\ - p - q = p \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} p = 1\ \ \ \\ q = - 2 \\ \end{matrix} \right.\ \]
\[\Longrightarrow x^{2} + x - 2 \Longrightarrow искомый\ \]
\[трехчлен.\]