Метод дихотомии решения алгебраический уравнений. Графическая интерпретация метода. Условие применимости

Метод деления отрезка пополам (дихотомии)                                                                                                                   Идея метода:                                                                                                           c=(a+b)/2.                        Если f(a) * f(с)<0, то корень  на отрезок [a, c], тогда деление отрезка можно повторить.                           В противном случае корень попал на половину [c, b], и необходимо изменить значение левого конца отрезка: a=c. Поскольку корень всегда заключен внутри отрезка, итерационный процесс можно останавливать, если длина отрезка станет меньше заданной точности:|b – a|< ε

SUB dih (a,b,l,root)                                                                                                  x=(a+b)/2                                                                                                                             do                                                                                                                                        If F(x)*F(a)<0 Then                                                                                                             b=x                                                                                                                                      ELSE                                                                                                                                    a=x                                                                                                                                   END If                                                                                                                         x=(a+b)/2                                                                                                                     LOOP Until (b-a)<e                                                                                                          root =x                                                                                                                                end sub