Definición y resolución general de ecuaciones de segundo grado

1. $a=1$, $b=2$, $c=-1$

$$\displaystyle x=\frac{-2 \pm \sqrt{1+4}}{2}= \frac{-2 \pm \sqrt{5}}{2}=\left \{\begin{matrix} x_1=-2,4142 \\ x_2=0,4142\end{matrix}\right.$$

2. $a=4$, $b=0$, $c=-16$

$$\displaystyle x=\frac{-0 \pm \sqrt{0+16\cdot16}}{2\cdot4}= \frac{\pm16}{8}=\left \{\begin{matrix} x_1=2 \\ x_2=-2\end{matrix}\right.$$

3. $a=3$, $b=6$, $c=0$

$$\displaystyle x=\frac{-6 \pm \sqrt{36-0}}{2\cdot3}= \frac{-6\pm6}{6}=\left \{\begin{matrix} x_1=0 \\ x_2=-2\end{matrix}\right.$$