Exercício Resolvido de Inequações
e)
\( -x^{2}+7x-12<0 \)
\[
\begin{gathered}
-x^{2}+7x-12=0\\[5pt]
\Delta=b^{2}-4ac=7^{2}-4.(-1).(-12)=49-48=1\\[5pt]
x=\frac{-b\pm\sqrt{\Delta \;}}{2a}=\frac{-7\pm \sqrt{1\;}}{2.(-1)}=\frac{-7\pm 1}{-2}\\[5pt]
x=3\qquad \text{ou}\qquad x=4
\end{gathered}
\]
\[ \bbox[#FFCCCC,10px]
{V=\left.\phantom{{}}\right]\;-\infty ;3\;\left[\phantom{{}}\right.\;\cup\;\left.\phantom{{}}\right]\;4;+\infty \;\left[\phantom{{}}\right.}
\]