生成具有根的总和和乘积的二次方程

给定两个整数S和M ，任务是找到二次方程的系数，使得根的和和乘积分别为S和M。

例子：

Input: S = 5, M = 6
Output: 1 -5 6
Explanation:
For the quadratic equation x² – 5x + 6 = 0. The root of the equation are 2 and 3. Therefore, the sum of roots is 2 + 3 = 5, and the product of roots is 2*3 = 6.

Input: S = -2, M = 1
Output: 1 2 1

方法：给定的问题可以通过使用二次方程的性质来解决，如下所示：

$aX^2 + bX + c = 0$

For the above quadratic equation the roots are given by:

$X = \frac{-b + \sqrt{b^2 - 4ac}}{2*a}$ and $X = \frac{-b - \sqrt{b^2 - 4ac}}{2*a}$

The sum of roots is given by:

=> $S = \frac{-b + \sqrt{b^2 - 4ac}}{2*a} + \frac{-b - \sqrt{b^2 - 4ac}}{2*a}$
=> $S = \frac{-2b}{2a}$
=> $S = \frac{-b}{a}$

The product of roots is given by:

$P = \frac{-b + \sqrt{b^2 - 4ac}}{2*a} * \frac{-b - \sqrt{b^2 - 4ac}}{2*a}$
=> $P = \frac{{-b}^2 - {(\sqrt{b^2 - 4ac})}^2}{4{a}^2}$
=> $P = \frac{c}{a}$

从以上两个等式中，如果a 的值为1，则b 的值为(-1)*S ，而c 的值为P 。因此，方程由下式给出：

$X^2 + (-1)*S*X + P = 0$

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to find the quadratic
// equation from the given sum and
// products of roots
void findEquation(int S, int M)
{
    // Print the coefficients
    cout << "1 " << (-1) * S << " "
         << M << endl;
}
 
// Driver Code
int main()
{
    int S = 5, M = 6;
    findEquation(S, M);
 
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
 
class GFG{
   
// Function to find the quadratic
// equation from the given sum and
// products of roots
public static void findEquation(int S, int M)
{
     
    // Print the coefficients
    System.out.println("1 " + ((-1) * S) + " " + M);   
}
 
// Driver code
public static void main(String[] args)
{
      int S = 5, M = 6;
       
    findEquation(S, M);
}
}
 
// This code is contributed by user_qa7r

Python3

# Python3 program for the above approach
 
# Function to find the quadratic
# equation from the given sum and
# products of roots
def findEquation(S, M):
     
    # Print the coefficients
    print("1 ", ((-1) * S), " " , M)
 
# Driver Code
S = 5
M = 6
 
findEquation(S, M)
 
# This code is contributed by Ankita saini

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Function to find the quadratic
// equation from the given sum and
// products of roots
public static void findEquation(int S, int M)
{
     
    // Print the coefficients
    Console.Write("1 " + ((-1) * S) + " " + M);  
}
 
// Driver code
static void Main()
{
    int S = 5, M = 6;
        
    findEquation(S, M);
}
}
 
// This code is contributed by code_hunt

Javascript

 
// Javascript program for the above approach
 
// Function to find the quadratic
// equation from the given sum and
// products of roots
function findEquation(S, M)
{
     
    // Print the coefficients
    document.write("1 " + ((-1) * S) + " " + M);   
}
 
// Driver Code
var S = 5, M = 6;
       
findEquation(S, M);
 
// This code is contributed by Ankita saini
 

输出：

1 -5 6

时间复杂度： O(1)
辅助空间： O(1)