Exercício Resolvido de Equações do 2.º Grau
e)
\( \displaystyle 8x^{2}+2x-1=0 \)
Calculando Δ
\[ \bbox[#99CCFF,10px]
{\Delta =b^{2}-4ac}
\]
\[
\begin{align}
& \Delta =2^{2}-4.8.(-1)\\
& \Delta =4+32\\
& \Delta=36
\end{align}
\]
Cálculo das raízes
\[ \bbox[#99CCFF,10px]
{x_{1,2}=\frac{-b\pm \sqrt{\Delta \;}}{2a}}
\]
\[
\begin{align}
& x_{1,2}=\frac{-2\pm\sqrt{36\;}}{2.8}\\
& x_{1,2}=\frac{-2\pm6}{16}\\
& x_{1}=\frac{-2+6}{16}=\frac{4:4}{16:4}=\frac{1}{4}\\
& x_{2}=\frac{-2-6}{16}=\frac{-8:8}{16:8}=-{\frac{1}{2}}
\end{align}
\]
\[ \bbox[#FFCCCC,10px]
{V=\left\{\frac{1}{4},-\frac{1}{2}\right\}}
\]