started analyzing t

documents/math-minimal-distance-to-cubic-function/quadratic-functions.tex

@@ -164,6 +164,10 @@ Otherwise, there is only one solution $x_1 = 0$.
 Let $t$ be defined as
 \[t := \sqrt[3]{\sqrt{3 \cdot (4 \alpha^3 + 27 \beta^2)} -9\beta}\]
 
+\subsubsection{Analyzing $t$}
+\input{analyzing-t.tex}
+
+\subsubsection{Solutions of $x^3 + \alpha x + \beta$}
 I will make use of the following identities:
 \begin{align*}
     (1-i \sqrt{3})^2     &= -2 (1+i \sqrt{3})\\