M$$ller$\text{'}$s method is a root finding method that uses three initial approximations, $p_0,p_1,$ and $p_2,$

and determines the next approximation $p_3$ by considering the intersection of the $x-$axis with

the parabola through $(p_0,f(p_0)),(p_1,f(p_1)),$ and $(p_2,f(p_2)).$ The algorithm considers three given

initial approximations $p_0,p_1$ and $p_2,$ and generate the value of $p_3$ based on the following

$p_3=p_2-\frac{2c}{b+sgn(b)\sqrt[\phantom{2}]{b^2-4ac}}$

where

$c=f(p_2)$

$b=\frac{(p_0-p_2{)}^2[f(p_1)-f(p_2)]-(p_1-p_2{)}^2[f(p_0)-f(p_2)]}{(p_0-p_2)(p_1-p_2)(p_0-p_1)}$

$a=\frac{(p_1-p_2)[f(p_0)-f(p_2)]-(p_0-p_2)[f(p_1)-f(p_2)]}{(p_0-p_2)(p_1-p_2)(p_0-p_1)}$

Then continue the iteration, with $p_1,p_2$ and $p_3$ replacing $p_0,p_1$ and $p_2.$

Write an M$-$file function that implements the M$$ller$\text{'}$s method for root$-$finding problem. The

input parameters should be : the function $f,$ three initial guesses, an error tolerance, and the

maximum number of iterations. The algorithm should stop when the approximate relative error

is less than or equal to the tolerance. Your output should be a table where each row contains the

number of iteration, the value of the root $p_n,$ and the approximate relative error.