Question

equação do segundo grau cujas raízes são menos 1 sobre 2 e 1 sobre 3

Answer 1

Use:  (x - x')(x - x'') = 0


$S = \left\{ -\dfrac{1}{2} ~~;~~ \dfrac{1}{3} \right\}\\\\\\ \left(x - \left(-\dfrac{1}{2} \right) \right) \left(x - \dfrac{1}{3} \right)=0 \to~~~~ \left(x +\dfrac{1}{2} \right) \left(x - \dfrac{1}{3} \right)=0 \to\\\\\\ x^2 - \dfrac{x}{3}+ \dfrac{x}{2}- \dfrac{1}{6}=0\to~~~~ mmc = 6\\\\\\ 6x^2-2x+3x-1=0\to~~~~ \large\boxed{~6x^2+x-1=0~}$

Answer 2

x² - Sx   + P = 0

===
x' = -1/2

x'' = 1/3

===
Soma das raízes

-1/2 + 1/3

-1/6

===
Produto das raízes

-1/2 . 1/3
-1/6

===
x² - Sx + P = 0

x² - (-1/6)x+ (-1/6)
x² + 1/6x  - 1/6
x² + x/6 - 1/6
x² + (x - 1) / 6
6x² +x - 1 / 6

=> 6x² + x - 1 = 0