# Generate Quadratic Equation having given sum and product of roots

• Last Updated : 04 May, 2021

Given two integers S and M, the task is to find the coefficients of the quadratic equation such that the sum and the product of the roots are S and M respectively.

Examples:

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

Approach: The given problem can be solved by using the property of the Quadratic Equation as shown below: For the above quadratic equation the roots are given by: and The sum of roots is given by:

=> => => The product of roots is given by: => => From the above two equations, if the value of a is 1 then the value of b is (-1)*S, and c is P. Therefore, the equation is given by: Below is the implementation of the above approach:

## 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

 

Output:

1 -5 6

Time Complexity: O(1)
Auxiliary Space: O(1)

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