\[\boxed{\text{674\ (674).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x^{2} + \frac{70}{12}x + \frac{a^{2} + 1}{12} = 0\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = - \frac{70}{12} \\ x_{1}x_{2} = \frac{a^{2} + 1}{12} \\ \end{matrix} \right.\ \]
\[так\ как\ - \frac{70}{12} < 0,\ то\ \]
\[x_{1} < 0,\ x_{2} < 0\ или\ \]
\[x_{1} < 0,\ x_{2} > 0;\]
\[так\ как\ \frac{a^{2} + 1}{12} > 0,\ то\]
\[x_{1} < 0;\ x_{2} < 0 -\]
\[что\ и\ требовалось\ доказать.\ \]