Question

determine o resultado da equação g(x) = -x²+4x-4 ​

Answer 1

................................

Answer 2

✅ Após resolver a equação do segundo grau, concluímos que suas raízes são:

    $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf x' = 2\:\:\:e\:\:\:x'' = 2\:\:\:}}\end{gathered} }$

Seja a função do segundo grau:

      $\Large\displaystyle\begin{gathered} g(x) = -x^2 + 4x - 4\end{gathered}$

Cujos coeficientes são:

                    $\Large\begin{cases} a = -1\\b = 4\\c = -4\end{cases}$

Calculando o delta, temos:

       $\Large\displaystyle\begin{gathered} \Delta = b^{2} - 4ac\end{gathered}$

             $\Large\displaystyle\begin{gathered} = 4^{2} - 4\cdot(-1)\cdot(-4)\end{gathered}$

             $\Large\displaystyle\begin{gathered} = 16 - 16\end{gathered}$

             $\Large\displaystyle\begin{gathered} = 0\end{gathered}$

Calculando as raízes, temos:

         $\Large\displaystyle\text{ \begin{gathered} x = \frac{-b\pm\sqrt{\Delta}}{2a}\end{gathered} }$

              $\Large\displaystyle\text{ \begin{gathered} = \frac{-4 \pm\sqrt{0}}{2\cdot(-1)}\end{gathered} }$

              $\Large\displaystyle\begin{gathered} = \frac{-4}{-2}\end{gathered}$

               $\Large\displaystyle\begin{gathered} = 2\end{gathered}$

✅ Portanto, suas raízes são:

       $\Large\displaystyle\begin{gathered} x' = 2\:\:\:e\:\:\:x'' = 2\end{gathered}$

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