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# Generate Quadratic Equation having given sum and product of roots

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 rootsvoid findEquation(int S, int M){    // Print the coefficients    cout << "1 " << (-1) * S << " "         << M << endl;} // Driver Codeint main(){    int S = 5, M = 6;    findEquation(S, M);     return 0;}

## Java

 // Java program for the above approachimport java.io.*; class GFG{   // Function to find the quadratic// equation from the given sum and// products of rootspublic static void findEquation(int S, int M){         // Print the coefficients    System.out.println("1 " + ((-1) * S) + " " + M);   } // Driver codepublic 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 rootsdef findEquation(S, M):         # Print the coefficients    print("1 ", ((-1) * S), " " , M) # Driver CodeS = 5M = 6 findEquation(S, M) # This code is contributed by Ankita saini

## C#

 // C# program for the above approachusing System; class GFG{ // Function to find the quadratic// equation from the given sum and// products of rootspublic static void findEquation(int S, int M){         // Print the coefficients    Console.Write("1 " + ((-1) * S) + " " + M);  } // Driver codestatic 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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