\[x^{2} + bx + c = 0\]
\[- \frac{1}{4}\ \ и\ \ \frac{1}{7}:\]
\[- b = - \frac{1}{4} + \frac{1}{7} = \frac{- 7 + 4}{28}\]
\[\ - b = - \frac{3}{28} \Longrightarrow b = \frac{3}{28}.\]
\[c = - \frac{1}{4} \cdot \frac{1}{7} \Longrightarrow \ c = - \frac{1}{28}.\]
\[Ответ:b = \frac{3}{28};\ \ c = - \frac{1}{28}.\]