TeX Quellcode:
\begin{array}{lrclcll} & \mathbb{D} &=& \mathbb{R} \cr\cr & (2x^3+8x^2-6x)(9x^3-10x) &=& 0 \cr\cr\text{Faktor 1:} & 2x^3+8x^2-6x &=& 0 \cr & x(2x^2+8x-6) &=& 0 &\vert& \text{Satz vom Nullprodukt} \cr\cr \text{Faktor 1.1:} & x_1 &=& 0 \cr\cr \text{Faktor 1.2:} & 2x^2+8x-6 &=& 0 &\vert& :2 \cr & x^2+4x-3 &=& 0 &\vert& \text{p-q-Formel} \cr & x_{2,3} &=& -\dfrac42\pm\sqrt{\left(\dfrac42\right)^2+3} \cr& x_{2,3} &=& -2\pm\sqrt{7} \cr\cr & x_2 &=& -2+\sqrt{7} \approx 0{,}65 \cr\cr & x_3 &=& -2-\sqrt{7} \approx -4{,}65 \cr\cr\text{Faktor 2:} & 9x^3-10x &=& 0 \cr & x(9x^2-10) &=& 0 &\vert& \text{Satz vom Nullprodukt} \cr\cr \text{Faktor 2.1:} & x_4 &=& 0 \cr\cr \text{Faktor 2.2:} & 9x^2-10 &=& 0 &\vert& +10 \cr & 9x^2 &=& 10 &\vert& :9 \cr & x^2 &=& \dfrac{10}{9} &\vert& \pm\sqrt{} \cr & x_{5,6} &=& \pm\sqrt{\dfrac{10}{9}} \approx \pm 1{,}05 \cr\cr & \mathbb{L} &=& \left\{-2-\sqrt{7};-\sqrt{\dfrac{10}{9}};0;-2+\sqrt{7};\sqrt{\dfrac{10}{9}}\right\}\end{array}