TeX Quellcode:
\begin{array}{crclcl} & 0 &=& 4z^3 +20 z^2 +50z \cr & 0 &=& 4z \left( z^2 +5z + \dfrac{25}{2}\right) &\vert& \text{Satz vom Nullprodukt} \cr\cr \text{Faktor 1:} & 4z &=& 0 &\vert& : 4 \cr & z_1 &=& 0 \cr\cr\cr \text{Faktor 2:} & 0 &=& z^2+5z+\dfrac{25}{2} &\vert& \text{p-q-Formel} \cr\cr & z_{2,3} &=& -\dfrac{5}{2} \pm \sqrt{\left(\dfrac{5}{2}\right)^2-\dfrac{25}{2}} \cr\cr& &=& -\dfrac{5}{2} \pm \sqrt{-\dfrac{25}{4}}\cr\cr & &=& -\dfrac{5}{2} \pm \sqrt{-1\cdot\dfrac{25}{4}}\cr\cr& &=& -\dfrac{5}{2} \pm \dfrac{5}{2}\sqrt{-1} &\vert& \sqrt{-1}=i \cr \cr\cr & z_2 &=& -\dfrac{5}{2}+\dfrac{5}{2}i \cr\cr & z_3 &=& -\dfrac{5}{2}-\dfrac{5}{2}i \cr \cr\cr & \mathbb{L} &=& \left\{ 0 \; ; \; -\dfrac{5}{2}+\dfrac{5}{2}i \; ; \; -\dfrac{5}{2}-\dfrac{5}{2}i\right\} \end{array}