Observe que:
[tex]\text{x}=\dfrac{-\text{b}\pm\sqrt{\text{b}^2-4\cdot\text{a}\cdot\text{c}}}{2\text{a}}[/tex]
Onde, [tex]\Delta=\text{b}^2-4\cdot\text{a}\cdot\text{c}[/tex]
a) [tex]-\text{x}^2+\text{x}+12=0[/tex]
Temos [tex]\text{a}=-1, \text{b}=1[/tex] e [tex]\text{c}=12[/tex]
Logo, [tex]\text{x}=\dfrac{-1\pm\sqrt{1^2-4\cdot(-1)\cdot12}}{2\cdot(-1)}=\dfrac{-1\pm7}{-2}[/tex]
Desta maneira, as raízes são:
[tex]\text{x}'=\dfrac{-1+7}{-2}=\dfrac{6}{-2}=-3[/tex]
[tex]\text{x}'=\dfrac{-1-7}{-2}=4[/tex]
[tex]\text{S}=\{-3, 4\}[/tex]
b) [tex]-\text{x}^2+6\text{x}-5=0[/tex]
[tex]\text{x}=\dfrac{-6\pm\sqrt{6^2-4\cdot(-1)\cdot(-5)}}{2\cdot(-1)}=\dfrac{-6\pm4}{-2}[/tex]
As raízes são:
[tex]\text{x}'=\dfrac{-6+4}{-2}=\dfrac{-2}{-2}=1[/tex]
[tex]\text{x}''=\dfrac{-6-4}{-2}=\dfrac{-10}{-2}=5[/tex]
[tex]\text{S}=\{1, 5\}[/tex]
