function [q,x] = m_newton(p,x,eps,N)
%
%  Applies a modified Newton's method on (x-1)^d,
%  modefied to take the multiplicity into account.
%
n = size(p,2);
d = [1 -x];
[q,r] = deconv(p,d);
% fprintf('  real(x)               imag(x)                 dx        f(x) \n');
for i = 1:N
   [q1,r1] = deconv(q,d);
   dx = r(n)/r1(n-1);
   x = x - (n-1)*dx;
   d(2) = -x;
   [q,r] = deconv(p,d);
%   fprintf('%.15e %.15e  %.2e  %.2e\n', real(x), imag(x), dx, r(n));
   if (abs(dx) < eps) | (abs(r(n)) < eps)
%      fprintf('succeeded after %d steps\n', i);
      return;
   end
end
fprintf('failed requirements after %d steps\n', N);