По теореме Виета:

[tex] {x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c [/tex]

[tex] {x}^{2} + 10x - 4 = 0 \\ x_{1} + x_{2} = - 10 \\ x_{1} x_{2} = - 4 \\ \frac{1}{x_{1}} + \frac{1}{x_{2}} = \frac{x_{1} + x_{2}}{x_{1}x_{2}} = \frac{ - 10}{ - 4} = \frac{5}{2} = 2.5[/tex]