C++ 求二次方程的所有根程序

对于二次方程 ax²+bx+c = 0（其中 a、b 和 c 是系数），其根由以下公式给出。

项 b2-4ac 被称为二次方程的判别式。判别式决定了根的性质。

• 如果判别式大于 0，则根为实数且不相等。
• 如果判别式等于 0，则根为实数且相等。
• 如果判别式小于 0，则根为复数且不相等。

示例：二次方程的根

#include <iostream>
#include <cmath>
using namespace std;

int main() {

    float a, b, c, x1, x2, discriminant, realPart, imaginaryPart;
    cout << "Enter coefficients a, b and c: ";
    cin >> a >> b >> c;
    discriminant = b*b - 4*a*c;
    
    if (discriminant > 0) {
        x1 = (-b + sqrt(discriminant)) / (2*a);
        x2 = (-b - sqrt(discriminant)) / (2*a);
        cout << "Roots are real and different." << endl;
        cout << "x1 = " << x1 << endl;
        cout << "x2 = " << x2 << endl;
    }
    
    else if (discriminant == 0) {
        cout << "Roots are real and same." << endl;
        x1 = -b/(2*a);
        cout << "x1 = x2 =" << x1 << endl;
    }

    else {
        realPart = -b/(2*a);
        imaginaryPart =sqrt(-discriminant)/(2*a);
        cout << "Roots are complex and different."  << endl;
        cout << "x1 = " << realPart << "+" << imaginaryPart << "i" << endl;
        cout << "x2 = " << realPart << "-" << imaginaryPart << "i" << endl;
    }

    return 0;
}

输出

Enter coefficients a, b and c: 4
5
1
Roots are real and different.
x1 = -0.25
x2 = -1

在此程序中，sqrt() 库函数用于查找数字的平方根。