\[x^{2} + px + 12 = 0\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = - p\ \\ x_{1} \cdot x_{2} = q\ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ \ \ } \right.\ \left\{ \begin{matrix} x_{1} + x_{2} = - p \\ x_{1} \cdot x_{2} = 12\ \ \ \\ \end{matrix} \right.\ \]
\[1 \cdot 12 = 2 \cdot 6 = 3 \cdot 4 = 4 \cdot 3 = 6 \cdot 2 =\]
\[= 12 \cdot 1 = 12\]
\[p_{1} = 1 + 12 = 13;\text{\ \ \ \ }\]
\[p_{2} = 2 + 6 = 8;\text{\ \ \ }\]
\[p_{3} = 3 + 4 = 7.\]
\[Ответ:\ \ p = \left\{ - 7;\ - 8;\ - 13 \right\}.\]