The Muller method is used to find the roots of polynomial equations. It estimates roots by determining the intersection of a line through two y-values of the function with the x-axis. The method improves on the secant method by fitting a parabola through three points instead of a line, allowing a more accurate estimated root to be calculated using the quadratic formula. Specifically, it generates a system of equations from three points to solve for the coefficients of the parabola, then finds where it intersects the x-axis to give a new estimated root.

1. 1MULLER METHODJeannie Castaño 2053298

2. This is a method to find the roots of equations polynomials in the general way: Where n is the order of the polynomial and they are they constant coefficients. Continuing with the polynomials, these they fulfill the following rules: " For the order equation n, is n real or complex roots. It should be noticed that those roots are not necessarily different. " If n is odd, there is a real root at least. " If the complex roots exist, a conjugated couple exists.

3. DEFINITIONIt is the method secant, which obtains roots, estimating a projection of a direct line in the axis x, through two values of the function.The method consists on obtaining the coefficients of the three points, to substitute them in the quadratic formula and to obtain the point where the parable intercepts the axis x.

4. f(x)Línea rectaxRaíz estimadaxxXX1X0Raíz

5. Raíz estimadaf(x)Parábola000Raíz xxXX2X0X1This way, this parable is looked for intersectorthe three points [x0, f(x0)], [x1, f(x1)] and [x2, f(x2)].

6. The last equation generates that , this way, one can have a system of two equations with two incognito:Defining this way: Substituting in the system:

7. Having the coefficients as a result: Finding the root, you to implement the conventional solution, but due to the error of rounding potential, an alternative formulation will be used:Error

8. h = 0,1x2 = 5 x1 = 5,5 x0 =4,5

9. BIBLIOGRAGHYhttp://lc.fie.umich.mx/~calderon/programacion/Mnumericos/Muller.htmlhttp://aprendeenlinea.udea.edu.co/lms/moodle/mod/resource/view.php?id=24508