# C++ 程序：查找二次方程式的所有根 > 原文： [https://www.programiz.com/cpp-programming/examples/quadratic-roots](https://www.programiz.com/cpp-programming/examples/quadratic-roots) #### 該程序從用戶那里接受二次方程式的系數，并顯示根（實數根和復數根都取決于判別式）。 要理解此示例，您應該了解以下 [C++ 編程](/cpp-programming "C++ tutorial")主題： * [C++ `if`，`if...else`和嵌套`if...else`](/cpp-programming/if-else) * * * 對于二次方程`ax ^ 2 + bx + c = 0`（其中`a`，`b`和`c`為系數），其根由以下公式給出。  術語`b^2-4ac`被稱為二次方程的判別式。 判別式說明了根的性質。 * 如果判別式大于 0，則根是實數且不同。 * 如果判別式等于 0，則根是實數且相等。 * 如果判別式小于 0，則根是虛數且不同。  * * * ## 示例：二次方程的根 ```cpp #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 + sqrt(discriminant)) / (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; } ``` **輸出** ```cpp 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()`庫函數用于查找數字的平方根。