TeX Quellcode:

\begin{array}{crclcl} & 0 &=& x^3-\dfrac{7}{12}x^2-\dfrac{5}{24}x &\vert& \text{ausklammern} \cr & 0 &=& x \left(x^2-\dfrac{7}{12}x-\dfrac{5}{24} \right) &\vert& \text{Satz vom Nullprodukt} \cr \text{Faktor 1:} & x_1 &=& 0 \cr\cr \text{Faktor 2:} & x^2-\dfrac{7}{12}x-\dfrac{5}{24} &=& 0 &\vert& \text{p-q-Formel} \cr\cr& x_{2,3} &=& -\left(-\dfrac{7}{24}\right) \pm \sqrt{\left(-\dfrac{7}{24}\right)^2+\dfrac{5}{24}} \cr\cr & &=& \dfrac{7}{24} \pm \sqrt{\dfrac{49}{576}+\dfrac{120}{576}} \cr\cr & &=& \dfrac{7}{24} \pm \sqrt{\dfrac{169}{576}} \cr\cr & &=& \dfrac{7}{24} \pm \dfrac{13}{24} \cr \cr & x_2 &=& \dfrac{7}{24} + \dfrac{13}{24} = \dfrac{20}{24} = \dfrac{5}{6} \cr\cr & x_3 &=& \dfrac{7}{24} - \dfrac{13}{24} = -\dfrac{6}{24} = -\dfrac{1}{4} \end{array}