Les structures Conditionnelles

 Mise à jour le : 01/11/2004

Énoncé
Écrire un programme Pascal qui permet de résoudre l'équation de la forme Ax2+BX+C=0. 

I) La préanalyse :



II) L'analyse :

Nom = EquationDeg2

Séquences Liste des définitions Explicites Objets Utilisés
 4 Résultat = Si A=0  
                               Alors  
                                              Si B=0                     
                                                  Alors A
                                                               Si C=0     B
                                                                      Alors                                                 C
                                                                                 Ecrire ("La solution est IR") Delta 
                                                                     Sinon  X1
                                                                                 Ecrire ("La solution est Vide") X2
                                                                FinSi   
                                                Sinon  
                                                           Ecrire (-C/B)  
                                         FinSi   
                               Sinon  
                                          Delta ß   Carré(B) - 4*A*C  
                                            Si Delta<0  
                                                    Alors  
                                                            Ecrire ("La solution est Vide")   
                                                    Sinon  
                                                         Si Delta=0  
                                                              Alors  
                                                                     Ecrire (-B/(2*A))   
                                                               Sinon  
                                                                      x1ß    (-B+Racine(delta))/(2*A)  
                                                                      x2ß    (-B-Racine(delta))/(2*A)  
                                                                      Ecrire ("Deux racines :",x1, X2)  
                                                       FinSi   
                                        FinSi   
                 Finsi  
1 Lire(A)   
2 Lire(B)   
3 Lire(C)   
5 Fin EquationDeg2  
III) Le tableau de déclaration des objets :
Objets Utilisés Nature/Type Rôle
A variable/Réel

La 1ère coef. de l'équation

B variable/Réel

La 2ème coef. de l'équation

C variable/Réel

La 3ème coef. de l'équation

Delta variable/Réel La valeur du déterminant
X1 variable/Réel Racine 1
X2 variable/Réel Racine 2
IV) L'algorithme :
0- Début EquationDeg2
1- Lire (A)
2- Lire (B)
3- Lire (C)
4-
              Si A=0
                               Alors
                                       Si B=0                   
                                                  Alors
                                                      Si C=0    
                                                           Alors                                               
                                                                 Ecrire ("La solution est IR")
                                                            Sinon
                                                                 Ecrire ("La solution est Vide")
                                                         FinSi 
                                                Sinon
                                                           Ecrire (-C/B)
                                         FinSi 
                               Sinon
                                          Delta ß    Carré(B) - 4*A*C
                                          Si Delta<0
                                                    Alors
                                                            Ecrire ("La solution est Vide") 
                                                    Sinon
                                                           Si Delta=0
                                                                Alors
                                                                      Ecrire (-B/(2*A)) 
                                                                Sinon
                                                                      X1ß    (-B+Racine(delta))/(2*A)
                                                                      X2ß    (-B-Racine(delta))/(2*A)
                                                                      Ecrire ("Deux racines :",X1, X2)
                                                            FinSi 
                                        FinSi 
                 Finsi
5- Fin EquationDeg2
 
V) La traduction en turbo pascal :
Program Equation_Deg2;
uses Wincrt;
Var A,B,C,X1,X2,Delta : Real;
Begin
	Write('A=');
	Readln(A);
	Write('B=');
	Readln(B);
	Write('C=');
	Readln(C);
	If   A=0
	        Then
	            If   B=0
		        Then
	                             If   C=0
		                        Then
			                  Write('La solution est : IR')
		                        Else
			                   Write('La solution est : Vide')
	                      Else
		                   Write('La solution est : ' -C/B:5:2)
	         Else
                          Begin
		        Delta : = Sqr(B) - 4*A*C;
	                     If   Delta<0
		                Then
			          Write('La solution est : Vide')
	                             Else
	                                   If   Delta=0
		                                Then
			                           Write('La solution est : ', -B/(2*A):5:2)
				       Else
					Begin
                                                                        X1 : =  (-B+Sqrt(delta))/(2*A);
                                                                        X2 : =  (-B-Sqrt(delta))/(2*A);
					        Write ('Deux racines : ',X1:5:2,'  et  ', X2:5:2);
					End;
                          End;
End.

 

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