Question

Equação de 2°grau
x²+5x=0
​

Answer 1

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    $x^{2} \ + \ 5x \ = \ 0$           ⇒     $a \ = \ 1 \ \ ; \ \ \ \ \ b \ \ = \ 5 \ \ ; \ \ \ \ \ c \ = \ 0$

 

   $\Delta \ = \ b^{2} \ - \ 4ac \\\\ \Delta \ = \ 5^2 \ - \ 4 \ . \ 1 \ . \ 0 \\\\ \Delta \ = \ 25$

   $x \ = \ \frac{-b \ \ \± \ \ \sqrt{\Delta}}{2a} \\\\ x \ = \ \frac{-5 \ \ \± \ \ \sqrt{25}}{2 \ . \ 1} \\\\ x \ = \ \frac{-5 \ \ \± \ \ 25 }{2}$

•    $x' \ = \ \frac{-5 \ + \ 25}{2} \ \ \ \ \ \ \ \Rightarrow \ \ \ \ \ \ \ x' \ = \ \frac{20}{2} \ \ \ \ \ \ \Rightarrow \ \ \ \ \ \ \boxed{ \ \ x' \ = \ 10 \ \ }$  

•    $x'' \ = \ \frac{-5 \ - \ 25 \ }{2} \ \ \ \ \ \Rightarrow \ \ \ \ \ x'' \ = \ -\frac{30}{2} \ \ \ \ \ \Rightarrow \ \ \ \ \ \boxed{ \ \ x'' = \ -15 \ \ }$

RESPOSTA:

⇒   $\sf S \ = \ \{ \ 10 , \ -15 \ \}$

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