function [ x,k ] = Jarratt(p, x0, tol,Max_iter)
% STOP: |x-x0|<=tol, l<= Max_iter
% x0- beginning approximation, k- number of iterations
% Newton's method for findig roots of polynomial w(x), where
% w(x)=p(1)x^n+...+p(n)x + p(n+1).

k=0; %k- number of iterations
t= tol+1; % iterations
dp=polyder(p); %function derivative
%Jarrat method
while (abs(t)>tol)&& (k<= Max_iter),
        k=k+1;

        %calculating the value of a function for given x0 as an argument
        w0 = horner1(p,x0);
        %calculating the value of a function derivative for given x0 as an
        %argument
        dw = horner1(dp,x0);
        %checks if the value of function derivative at point x0 is equal
        %to zero, if it is the method will fail
        if dw==0,
            disp('Derivative is equal to zero!');
            return;
        end
        %calculating the value of a function derivative
        %for given x0 - 0.5*(w0/dw) as an argument
        t=w0/dw;
        d=horner1(dp,x0  - 0.5*t);
        %checks if the value of function derivative
        %at point  x0 - 0.5*(w0/dw) is equal to zero
        %if it is the method will fail
        if d==0,
            disp('Derivative is equal to zero');
            return;
        end
        x = x0 - (w0/horner1(d,x0));
        x0=x;
end
x=x0;
end