一元三次方程求根程序算法如下：算法來源：/albums/428969/428969/0/0.html#0$f703738da9773912a5584298f8198618377ae2c9C程序如下：#include<stdio.h>#include<math.h>main(){doublea,b,c,d;doubleA,B,C,L,K,T,rad;doubleGS1,GS2,Y1,Y2,P1,P2;doubleX1,X2,X3;//---------------------------------------------------------------------printf("請輸入a,b,c,d：");scanf("%lf,%lf,%lf,%lf",&a,&b,&c,&d); printf("\n");printf("a=%.2fb=%.2fc=%.2fd=%.2f\n\n",a,b,c,d); A=b*b-3*a*c;B=b*c-9*a*d;C=c*c-3*b*d;printf("A=%.3fB=%-7.3fC=%-7.3f\n\n",A,B,C);L=B*B-4*A*C;//判別式printf("L=%.3f\n\n",L);//---------------------------------------------------------------------if(A==0&&B==0) {X1=X2=X3=-b/(3*a); printf("X1=X2=X3=%.3f\n",X1); }//---------------------------------------------------------------------else{if(L>0) {Y1=A*b+(3*a*(-B+sqrt(L)))/2;Y2=A*b+(3*a*(-B-sqrt(L)))/2; printf("Y1=%.2fY2=%.2f\n\n",Y1,Y2); if(Y1>0) GS1=pow(Y1,1.0/3);//GS1為三次根號Y1 else GS1=-pow(fabs(Y1),1.0/3); if(Y2>0) GS2=pow(Y2,(1.0/3));//GS2為三次根號Y2 else GS2=-pow(fabs(Y2),(1.0/3));P1=(-2*b+GS1+GS2)/(6*a); P2=sqrt(3)*(GS1-GS2)/(6*a); X1=(-b-GS1-GS2)/(3*a); printf("X1=%.3f\n",X1); printf("X2=%.3f+%.3fi\n",P1,P2); printf("X3=%.3f-%.3fi\n",P1,P2); }//---------------------------------------------------------------------elseif(L==0){K=B/A;X1=-b/a+K; X2=X3=-K/2; printf("X1=%.3f\n",X1); printf("X2=X3=%.3f\n",X2);}//---------------------------------------------------------------------else { T=(2*A*b-3*a*B)/(2*pow(A,1.5));//A>0rad=acos(T);X1=(-b-2*sqrt(A)*cos(rad/3))/(3*a);X2=(-b+sqrt(A)*(cos(rad/3)+sqrt(3)*sin(rad/3)))/(3*a);X3=(-b+sqrt(A)*(cos(rad/3)-sqrt(3)*sin(