\[\boxed{\text{766.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[7x^{2} + bx - 23 = 0\ \ \ \ \ \ \ \ \ \ |\ :7\]
\[x^{2} + \frac{b}{7}x - \frac{23}{7} = 0\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = - \frac{b}{7} \\ x_{1}x_{2} = - \frac{23}{7}\text{\ \ \ } \\ \end{matrix} \right.\ \ \]
\[x_{1} > 0\]
\[x_{2} < 0\]
\[Что\ и\ требовалось\ доказать.\ \]