\[x^{2} - 3x - 7 = 0\]
\[x_{1} + x_{2} = 3;\ \ \ \ \ x_{1}x_{2} = - 7\]
\[\frac{1}{x_{1}} + \frac{1}{x_{2}} = \frac{x_{1} + x_{2}\ }{x_{1}x_{2}} = \frac{3}{- 7} = - \frac{3}{7}\]
\[\frac{1}{x_{1}} \cdot \frac{1}{x_{2}} = \frac{1}{x_{1}x_{2}} = \frac{1}{- 7} = - \frac{1}{7}\]
\[x^{2} + \frac{3}{7}x - \frac{1}{7} = 0.\]