# 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 = 6Output:1 -5 6Explanation:

For the quadratic equation x^{2}– 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 = 1Output: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 <bits/stdc++.h>` `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

`<script>` `// 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` `</script>` |

**Output:**

1 -5 6

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