This program will find or approximate  roots of any given polynomial.  In addition, it performs integration, derivation, maximum and minimum value searchings.  Basically, this program looks for all possible real roots of a polynomial, or P(x) = 0 and P(x) = c_n xⁿ + c_n-1 x^n-1 + ...+c₁ x + c₀ .  The user is asked to input the power of polynomial (degree) and the appropriate coefficients (c₀, c₁, c₂ ... c_n-1, c_n) based on the power entered. Then, this program finds roots of a polynomial by using a numerical method for a power higher than 2 and a direct root solving method for a power equals or less than 2.  For a polynomial power greater than 2 the user needs to enter an interval limit (a, and b where a < b) followed by a increment size (step) in order for the root approximation to work. The way this program approximates the roots is to take the average of the two closest values where the polynomial value changes from positive to negative or vice versa in a given range with a given step size.  Moreover, the program will proceed to integration, derivation, maximum/minimum value findings if the user wants to by typing a "1".  For the maximum/minimum value searching, again the user will be asked to enter an interval limit (a, and b where a < b). In order to do this real root approximation, the program will contain the following:

       ** Inheritance **
               Base Class(es)                                                  Derived Classes(es)
                Roots                                                                  RealRoot
                                                                                           RootError
                Polynomial                                                         Degree_N
                                                                                           Degree_2
                                                                                           Degree_1
 

       ** Virtual Functions & Polymorphism **
               Functions                                                           Data Members
               Polynomial                                                         Integrate, Derive, Max, Min, Find_Root
 
       ** Other variables **
               Symbol                                                               Definition
                a                                                                        lower limit of interval entered by user
                b                                                                        upper limit of interval entered by user
                n (integer)                                                          number of subintervals between "a" and "b"
                step                                                                    size of increment
                degree (integer)                                                 power of the polynomial
 
    Note:  All types are double unless indicated otherwise.