求方程ax 2 +bx+c=O的根，用3个函数分别求当：b2-4ac大于0、等于0和小于0时的根并 输出结果。从主函数输入a、b、c 的值。

可以使用以下三个函数分别求解二次方程的根：

1. 当 $b^2 - 4ac > 0$ 时，二次方程有两个不相等的实根：

void quadratic_equation1(double a, double b, double c) {
    double delta = b * b - 4 * a * c;
    if (delta > 0) {
        double x1 = (-b + sqrt(delta)) / (2 * a);
        double x2 = (-b - sqrt(delta)) / (2 * a);
        cout << "x1 = " << x1 << ", x2 = " << x2 << endl;
    }
    else if (delta == 0) {
        double x = -b / (2 * a);
        cout << "x = " << x << endl;
    }
    else {
        cout << "This quadratic equation has no real roots." << endl;
    }
}

2. 当 $b^2 - 4ac = 0$ 时，二次方程有两个相等的实根：

void quadratic_equation2(double a, double b, double c) {
    double delta = b * b - 4 * a * c;
    if (delta > 0) {
        double x1 = (-b + sqrt(delta)) / (2 * a);
        double x2 = (-b - sqrt(delta)) / (2 * a);
        cout << "x1 = " << x1 << ", x2 = " << x2 << endl;
    }
    else if (delta == 0) {
        double x = -b / (2 * a);
        cout << "x1 = x2 = " << x << endl;
    }
    else {
        cout << "This quadratic equation has no real roots." << endl;
    }
}

3. 当 $b^2 - 4ac < 0$ 时，二次方程没有实根，而是有两个共轭复数解：

void quadratic_equation3(double a, double b, double c) {
    double delta = b * b - 4 * a * c;
    if (delta > 0) {
        double x1 = (-b + sqrt(delta)) / (2 * a);
        double x2 = (-b - sqrt(delta)) / (2 * a);
        cout << "x1 = " << x1 << ", x2 = " << x2 << endl;
    }
    else if (delta == 0) {
        double x = -b / (2 * a);
        cout << "x1 = x2 = " << x << endl;
    }
    else {
        double real = -b / (2 * a);
        double imaginary = sqrt(-delta) / (2 * a);
        cout << "x1 = " << real << " + " << imaginary << "i, ";
        cout << "x2 = " << real << " - " << imaginary << "i" << endl;
    }
}

将以上三个函数整合到主函数中，可以实现输入 $a$、$b$、$c$ 的值，并根据 $b^2 - 4ac$ 的值调用相应的函数求解二次方程的根：

#include <iostream>
#include <cmath>

using namespace std;

void quadratic_equation1(double a, double b, double c) {
    double delta = b * b - 4 * a * c;
    if (delta > 0) {
        double x1 = (-b + sqrt(delta)) / (2 * a);
        double x2 = (-b - sqrt(delta)) / (2 * a);
        cout << "x1 = " << x1 << ", x2 = " << x2 << endl;
    }
    else if (delta == 0) {
        double x = -b / (2 * a);
        cout << "x = " << x << endl;
    }
    else {
        cout << "This quadratic equation has no real roots." << endl;
    }
}

void quadratic_equation2(double a, double b, double c) {
    double delta = b * b - 4 * a * c;
    if (delta > 0) {
        double x1 = (-b + sqrt(delta)) / (2 * a);
        double x2 = (-b - sqrt(delta)) / (2 * a);
        cout << "x1 = " << x1 << ", x2 = " << x2 << endl;
    }
    else if (delta == 0) {
        double x = -b / (2 * a);
        cout << "x1 = x2 = " << x << endl;
    }
    else {
        cout << "This quadratic equation has no real roots." << endl;
    }
}

void quadratic_equation3(double a, double b, double c) {
    double delta = b * b - 4 * a * c;
    if (delta > 0) {
        double x1 = (-b + sqrt(delta)) / (2 * a);
        double x2 = (-b - sqrt(delta)) / (2 * a);
        cout << "x1 = " << x1 << ", x2 = " << x2 << endl;
    }
    else if (delta == 0) {
        double x = -b / (2 * a);
        cout << "x1 = x2 = " << x << endl;
    }
    else {
        double real = -b / (2 * a);
        double imaginary = sqrt(-delta) / (2 * a);
        cout << "x1 = " << real << " + " << imaginary << "i, ";
        cout << "x2 = " << real << " - " << imaginary << "i" << endl;
    }
}

int main() {
    double a, b, c;
    cout << "Enter the coefficients of the quadratic equation: ";
    cin >> a >> b >> c;

    double delta = b * b - 4 * a * c;
    if (delta > 0) {
        quadratic_equation1(a, b, c);
    }
    else if (delta == 0) {
        quadratic_equation2(a, b, c);
    }
    else {
        quadratic_equation3(a, b, c);
    }

    return 0;
}