Graphical and analytical study of complex roots of the cubic equation with a parameter
The article deals with real and complex roots of the cubic equation with one parameter. Graphic dependences of these roots on the real parameter, as well as their asymptotic behavior are presented, without using explicit formulas for the roots of cubic equation in which they are expressed via the parameter, but on the contrary, considering the parameter as a function of the roots. The graphic dependence of these roots on the complex parameter is also presented on the complex plane. It constitutes a nomogram for the approximate determination of all three complex roots for any value of the complex parameter. The material can be useful to teachers, and used by them for additional classes with the students.