Computational Experiment Approach to Equations with Parameters

Abstract

In this chapter, different types of equations with parameters will be considered. In Chap. 3, we have investigated the influence of parameters/coefficients of quadratic functions on their properties. Some problems of that kind demonstrated the need to investigate a two-variable equation of the form f(x, a) = 0 representing a family of equations in regard to the variable x whose every element corresponds to a unique value of variable a, which, in this case, is called the parameter of the equation. In this chapter, the computational experiment approach is applied to three basic types of equations with parameters: equations containing absolute values of variables and parameters, equations containing variables and parameters under radicals, and equations containing transcendental functions of variables and parameters. In addition, the approach is used for exploring simultaneous equations in two variables with parameters.