Question

a soma dos inversos das raizes da equação
${2x }^{2} + 4x - 31 = 0$

Answer 1

 Se as raízes são x' e x''

soma dos inversos

$\frac{1}{x'} + \frac{1}{x"} = \\ \\ mmc=x'.x" \\ \\ \frac{x"+x'}{x'.x"} = \\ \\ se~~~a=2~~~~b=4~~~~c=-31 \\ \\ x'+x"=- \frac{b}{a} = \frac{-4}{2} =-2 \\ \\ x'.x"= \frac{c}{a} =- \frac{31}{2}$  

logo

$\frac{-2}{- \frac{31}{2} } =-2\times(- \frac{2}{31} )=+ \frac{4}{31} \\ \\ A~~soma~~dos~~inversos~~das~~ra\'izes\mapsto \frac{4}{31}$