Question

dada a função, determine o K para: f(x)=x³+Kx²-2x+5 sendo : f(2) = f(0)​

Answer 1

$k = -1$

$Calculando-se f(0):\\\\f(x)=x^3+Kx^2-2x+5\\\\f(0) = 0^3 + k.0^2 - 2.0 + 5\\\\f(0) = 5$

$Calculando-se f(2):$

$f(x)=x^3+Kx^2-2x+5\\\\f(2) = 2^3 +k.2^2 - 2.2 + 5\\\\f(2) = 8 + k.4 - 4 + 5\\\\f(2) = 4k + 9$

Igualando-se f(0) e f(2)  para obter o valor de k

$f(2) = f(0)\\\\4k + 9 = 5\\\\4k = 5 - 9\\\\4k = -4\\\\j = -4 / 4\\\\k = -1$

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Answer 2

✅ Após resolver os cálculos, concluímos que o valor do parâmetro "k" de modo que "f(2) = f(0)" é:

                                 $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf k = -1\:\:\:}}\end{gathered} }$

Seja a função cúbica:

                    $\Large\displaystyle\begin{gathered}\tt f(x) = x^{3} + kx^{2} - 2x + 5\end{gathered}$

Se estamos querendo calcular o valor de "k" de modo que "f(2) = f(0)", então, temos:

                                     $\Large\displaystyle\begin{gathered}\tt f(2) = f(0)\end{gathered}$

$\Large\displaystyle\begin{gathered}\tt 2^{3} + k\cdot2^{2} - 2\cdot2 + 5 = 0^{3} + k\cdot0^{2} - 2\cdot0 + 5\end{gathered}$

              $\Large\displaystyle\begin{gathered}\tt 8 + 4k - 4 + 5 = 0 + 0 - 0 + 5\end{gathered}$

                                         $\Large\displaystyle\begin{gathered}\tt 4k = 5 - 5 + 4 - 8\end{gathered}$

                                         $\Large\displaystyle\begin{gathered}\tt 4k = -4\end{gathered}$

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

                                             $\Large\displaystyle\begin{gathered}\tt k = -1\end{gathered}$

✅Portanto, o valor de "k" é:

                                             $\Large\displaystyle\begin{gathered}\tt k = -1\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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