原理參考-百度百科（http://baike.baidu.com/link?url=eA-bEvbcOBM2XmA4rzIG-lgci4MQdQcr7lCzCHBW-qG-qcPaDNovXp_jYxS2FUjlrOh1obH_D3Yv6ME2JYOxPyCgKhHIaXCHe-k9e69_c2tUxMTY90Z5-Oh9pZ-8LRf_）

先說一下中間出現的問題，開三次方的時候不能直接pow(x,1.0/3.0); 要分x大於零小於零，pow只接受大於零的引數。

另外，由於工程中只考慮實數，這裡複數沒有實現。

//cubicSolute.h

#pragma once
class cubicSolute
{
public:
	cubicSolute(void);
	~cubicSolute(void);
	void setCoefficient(double a,double b,double c,double d)//設方程係數
	{
		this->a =a;
		this->b =b;
		this->c =c;
		this->d =d;
	}
	void judge();
	double getX1(){return X1;}
	double getX2(){return X2;}
	double getX3(){return X3;}

private:
	double a,b,c,d;
	double A,B,C;
	double delt;//判別式
	double X1,X2,X3;
};
 

#include "cubicSolute.h"
#include <math.h>

cubicSolute::cubicSolute(void)
{
}


cubicSolute::~cubicSolute(void)
{
}

//Δ根的判別式
void cubicSolute::judge()
{
	A = pow(b,2)-3*a*c;
	B = b*c-9*a*d;
	C = pow(c,2)-3*b*d;
	delt = pow(B,2)-4*A*C;

	//當A=B=0時，公式1.+定理6
	if ((A==0&&B==0)||(delt==0&&A==0))
	{
		X1 = -b/(3*a);
		X2 = X1;
		X3 = X1;
	}

	//Δ=B2－4AC>0時，公式2
	if (delt>0)
	{
		double Y1 = A*b+3*a*((-B+pow(delt,0.5))/2);
		double Y2 = A*b+3*a*((-B-pow(delt,0.5))/2);
		//解決負數開三方出問題
		double Y1_three,Y2_three;
		if (Y1<0)
			Y1_three = - pow(-Y1,1.0/3.0);
		else
			Y1_three = pow(Y1,1.0/3.0);
		if (Y2<0)
			Y2_three = - pow(-Y2,1.0/3.0);
		else
			Y2_three = pow(Y2,1.0/3.0);
		X1 = (-b-(Y1_three+Y2_three))/(3*a);
		//X1,X2為複數，這裡不需要，未實現。
	}

	//當Δ=B2－4AC=0時，公式3
	if (delt==0&&(A!=0))
	{
		double K = B/A;
		X1 = -b/a + K;
		X2 = -K/2.0;
		X3 = X2;
	}

	//當Δ=B2－4AC<0時，公式4
	if (delt<0)
	{
		double T = (2*A*b-3*a*B)/(2*A*pow(A,0.5));//（A>0，－1<T<1）
		double theita = acos(T);
		X1 = (-b-2*pow(A,0.5)*cos(theita/3.0))/(3*a);
		X2 = (-b+pow(A,0.5)*(cos(theita/3.0)+pow(3,0.5)*sin(theita/3.0)))/(3*a);
		X3 = (-b+pow(A,0.5)*(cos(theita/3.0)-pow(3,0.5)*sin(theita/3.0)))/(3*a);
	}

}