EQUATION TROISIEME DEGRÉ CARDAN

import java.util.InputMismatchException;
import java.util.Scanner;

public class TroisiemeDeg {

	
	public static void main(String[] args) {
	
		boolean continuation=true;
		Scanner scan = new Scanner(System.in);
		double a,b,c,d,gDelta,x,y,z,im,re,u,v,p,q,m,n,theta,k;
		char verif;

  do{
	  System.out.println("\n\nax^3+bx^2+cx+d=0");
		System.out.println("Veuillez entrer les coefficients ");
	  
	  try{
		  
		  System.out.print("a = ");
			
			a= scan.nextDouble();
			while(a==0)	{
				System.out.println("a est different de 0!");
				System.out.print("a = ");
				a= scan.nextDouble();
			   }
			System.out.print("b = ");
			b= scan.nextDouble();  
			System.out.print("c = ");
			c= scan.nextDouble();
			System.out.print("d = ");
			d= scan.nextDouble();	
			System.out.println("\nl'equation a resoudre est : "+a+"x^3+"+b+"x^2+"+c+"x+"+d+"=0\n");
			
			p=(c/a)-(Math.pow(b, 2.0)/(3*Math.pow(a, 2.0)));
			q=((2*Math.pow(b, 3.0))/(27*Math.pow(a, 3.0)))-((b*c)/(3*Math.pow(a, 2.0)))+(d/a);
     		gDelta=4*Math.pow(p, 3.0)+27*Math.pow(q, 2.0);
     		m=((-q)/2)+(0.5)*Math.sqrt(gDelta/27);
     		n=((-q)/2)-(0.5)*Math.sqrt(gDelta/27);
     		u=Math.pow(Math.abs(m), 1.0/3);
     		v=Math.pow(Math.abs(n), 1.0/3);
					
		  if(gDelta>0)
		  {
			  if (m<0) u=-u;
			  if (n<0) v=-v;
			  x=u+v;
			  x+=(-b)/(3*a);
			  re=(-x)/2;
			  im=(Math.sqrt(3)/2)*(u-v);
			  re+=(-b)/(3*a);
			  System.out.println("1 racine reelle:\n    x = "+x+"");
			  System.out.println("2 racines complexes:\n" +
						"    y = "+re+"-"+im+"i , z  = "+re+"+"+im+"i");		
			  	  
		  }
			
			
		  else if(gDelta==0)
			{
			  
			  if(b==0&c==0&&d==0)
				  System.out.println("1 racine reelle de multiplicite 3:\n    x = y = z = 0 ");
			  else{
				x=(3*q)/p;
				x+=(-b)/(3*a);
				y=(-3*q)/(2*p);
				y+=(-b)/(3*a);
				
				System.out.println("1 racine reelle simple:\n    x = "+x+"");
				System.out.println("1 racine reelle double:\n    y = z = "+y+"");
			  }
				
			}
		  else
		  {
			  k=  (3*q)/((2*p)*Math.sqrt((-p)/3));               
			  theta=Math.acos(k);
			  x= 2*Math.sqrt((-p)/3)*Math.cos(theta/3);
			  y= 2*Math.sqrt((-p)/3)*Math.cos((theta+2*Math.PI)/3);
			  z= 2*Math.sqrt((-p)/3)*Math.cos((theta+4*Math.PI)/3);
			  if (x>-1E-6 && x< 1E-6) x=0.0;
			  if (y>-1E-6 && y< 1E-6) y=0.0;
			  if (z>-1E-6 && z< 1E-6) z=0.0;
			  x+=(-b)/(3*a);
			  y+=(-b)/(3*a);
			  z+=(-b)/(3*a);
			  System.out.println("3 racines reelles:\n    x = "+x+" , y = "+y+" , z = "+z+""); 
			  
			  
		  }
		  
		  
	  }
	  
	  catch (InputMismatchException e)
	    {
	    	System.out.println("Vous devez introduire un nombre");
	    	
	    }
	  
	  scan = new Scanner(System.in);
	   System.out.println("\nVoulez-vous continuer ? [o/n/?]");	
		 verif=scan.next().charAt(0);
		if (verif != 'o' && verif != 'O' && verif !='0')
		 continuation = false; 
	  
	  
  }while(continuation);
		
		
		

	}

}

06 juin 2008 17:33:59 :

j'ai rajouté le cas ou b=0,c=0 et d=0