unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;

type
  TForm1 = class(TForm)
    Label1: TLabel;
    Button1: TButton;
    Label2: TLabel;
    Label3: TLabel;
    Button2: TButton;
    procedure FormCreate(Sender: TObject);
    procedure Button2Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation
function f(x:real):real;
begin
f:=x*x*x*x+4.61*x*x*x-6.45*x*x-29.24*x+24.05
end;
function f1(x:real):real;
begin
f1:=4*x*x*x+13.83*x*x-12.9*x-29.24
end;
function f2(x:real):real;
begin
f2:=12*x*x+27.66*x-12.9
end;
{$R *.dfm}
procedure TForm1.FormCreate(Sender: TObject);
var x,x1,x0,a,b,e:real;
k:integer;
begin
e:=0.1;
a:=1;
b:=2;x:=2;
if f(b)*f2(x)>0 then
begin
k:=0;x1:=b;
repeat
x0:=x1;
k:=k+1;
x1:=x0-(f(x0)/f1(x0));
form1.Label1.Caption:=form1.Label1.Caption+intToStr(k)+' '+floattostr(x1)+''+formatfloat('#0.##########',abs(x0-x1))+#13;
while abs(x0-x1)<e
end;
else
begin
k:=0;
x1:=a;
repeat
x0:=x1;
k:=k+1;
x1:=x0-(f(x0)/f1(x0));
form1.Label1.Caption:=form1.Label1.Caption+inttostr(k)+' '+floattostr(x1)+' '+formatfloat('#0.######,'abs(x0-x1))+#13;
while abs(x0-x1)<e
end;
form1.Label3.Caption:=form1.Label3.Caption+'k'+' '+' '+' '+' |x0-x1|';
form1.Label2.Caption:=form1.Label2.Caption+'значение функции.---'+formatfloat('#0.##########',f(x1));
end;
procedure TForm1.Button2Click(Sender: TObject);
begin
close;
end;
end.