Cubical Hyperbola

$\begin{figure}\begin{center}\BoxedEPSF{CubicalHyperbola.epsf}\end{center}\end{figure}$

An equation of the form

$\begin{displaymath} y=ax^3+bx^2+cx+d, \end{displaymath}$

where the three Roots are Real and distinct, i.e.,

$\begin{eqnarray*} y&=&a(x-r_1)(x-r_2)(x-r_3)\\ &=&a[x^3-(r_1+r_2+r_3)x^2+(r_1r_2+r_1r_3+r_2r_3)x-r_1r_2r_3]. \end{eqnarray*}$