Lab09 due Wednesday November 17th Root finding by bisection and false position methods. For this lab your mission will consist in completing the functions 1) int bisection(double (*fct)(double x, void *par),void *par,double f0, double a, double b, double err, double *sol){ 2) int false_position(double (*fct)(double x, void *par),void *par,double f0, double a, double b, double err, double *sol){ In the file rootfind.cpp 1) The function bisection(double (*fct)(double x, void *par),void *par, double f0,double a, double b, double err, double *sol) evaluates the value of x such that fct(x,par)==f0 where par is a void pointer used to pass any parameters necessary to the calculation of the value of fct(). The root of the equation is searched for between a and b and is estimated with an accuracy specified by err. The root is returned via pointer sol. The algorithm used is bisection. The function returns -1 if there is an even number of root between a and b or is err is <=0. It returns 1 when the algorithm converges succesfully. Boundaries a and b can be specified in any order a>b or b>a. You just have to implement the bisection algorithm in this function. 2) The function false_position(double (*fct)(double x, void *par),void *par, double f0,double a, double b, double err, double *sol) works in the same way as bisection() except that the algorithm used is the false position which you need to implement. For this, it is suggested that you paste the content of bisection and change it a little to implement the false position. 3) Modify both your functions bisection() and false_position() using precompiler commands #ifdef and #endif in such a way that when VERBOSE is defined (-D VERBOSE in the compile command line) the number of iteration performed by each function is printed out. Observe that when the root is requested with a fine precision, fals_position() outperforms bisection. Is it always the case when you degrade the requested precision? Can you explain what is going on? To submit your work, use the command: submit p6720 Lab09 rootfind.cpp