# Find the quadratic equation from the given roots

Given the roots of a quadratic equation A and B, the task is to find the equation.

Note: The given roots are integral.

Examples:

Input: A = 2, B = 3
Output: x^2 – (5x) + (6) = 0
x2 – 5x + 6 = 0
x2 -3x -2x + 6 = 0
x(x – 3) – 2(x – 3) = 0
(x – 3) (x – 2) = 0
x = 2, 3

Input: A = 5, B = 10
Output: x^2 – (15x) + (50) = 0

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: If the roots of a quadratic equation ax2 + bx + c = 0 are A and B then it known that
A + B = – b * a and A * B = c * a.
Now, ax2 + bx + c = 0 can be written as
x2 + (b / a)x + (c / a) = 0 (Since, a != 0)
x2 – (A + B)x + (A * B) = 0, [Since, A + B = -b * a and A * B = c * a]
i.e. x2 – (Sum of the roots)x + Product of the roots = 0

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the quadratic ` `// equation whose roots are a and b ` `void` `findEquation(``int` `a, ``int` `b) ` `{ ` `    ``int` `sum = (a + b); ` `    ``int` `product = (a * b); ` `    ``cout << ``"x^2 - ("` `<< sum << ``"x) + ("` `         ``<< product << ``") = 0"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a = 2, b = 3; ` ` `  `    ``findEquation(a, b); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach  ` `class` `GFG  ` `{ ` `     `  `    ``// Function to find the quadratic  ` `    ``// equation whose roots are a and b  ` `    ``static` `void` `findEquation(``int` `a, ``int` `b)  ` `    ``{  ` `        ``int` `sum = (a + b);  ` `        ``int` `product = (a * b);  ` `        ``System.out.println(``"x^2 - ("` `+ sum +  ` `                           ``"x) + ("` `+ product + ``") = 0"``);  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String args[]) ` `    ``{  ` `        ``int` `a = ``2``, b = ``3``;  ` `     `  `        ``findEquation(a, b);  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function to find the quadratic ` `# equation whose roots are a and b ` `def` `findEquation(a, b): ` `    ``summ ``=` `(a ``+` `b) ` `    ``product ``=` `(a ``*` `b) ` `    ``print``(``"x^2 - ("``, summ,  ` `          ``"x) + ("``, product, ``") = 0"``) ` ` `  `# Driver code ` `a ``=` `2` `b ``=` `3` ` `  `findEquation(a, b) ` ` `  `# This code is contributed by Mohit Kumar `

## C#

 `// C# implementation of the above approach  ` `using` `System; ` `class` `GFG  ` `{ ` `     `  `    ``// Function to find the quadratic  ` `    ``// equation whose roots are a and b  ` `    ``static` `void` `findEquation(``int` `a, ``int` `b)  ` `    ``{  ` `        ``int` `sum = (a + b);  ` `        ``int` `product = (a * b);  ` `        ``Console.WriteLine(``"x^2 - ("` `+ sum +  ` `                          ``"x) + ("` `+ product + ``") = 0"``);  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main() ` `    ``{  ` `        ``int` `a = 2, b = 3;  ` `     `  `        ``findEquation(a, b);  ` `    ``}  ` `} ` ` `  `// This code is contributed by CodeMech. `

Output:

```x^2 - (5x) + (6) = 0
```

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