信息学奥赛一本通T1238-一元三次方程求解-题解(C++代码)

因为本题只要求 3个不同实根
所以根据（百度的）盛金公式
只要用第四种情况



根据公式写出代码如下：

#include<iostream>
#include<cmath>
#include<iomanip>
using namespace std;
int main()
{
    double a,b,c,d;
    double A,B,T,O;
    double x1,x2,x3;
    cin >> a >> b >> c >> d;
    A = b * b - 3 * a * c;
    B = b * c - 9 * a * d;
    T = (2 * A * b - 3 * a * B) / (2 * sqrt(A*A*A));
    O = acos(T);
    x1 = (-b - 2*sqrt(A)*cos(O/3)) / (3*a);
    x2 = (-b + sqrt(A)*(cos(O/3) + sqrt(3)*sin(O/3))) / (3*a);
    x3 = (-b + sqrt(A)*(cos(O/3) - sqrt(3)*sin(O/3))) / (3*a);
    //设置输出格式
    cout << fixed << setprecision(2) << x1 << " " 
         << fixed << setprecision(2) << x3 << " " 
         << fixed << setprecision(2) << x2 << " ";
    return 0;
}