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Find the quadratic equation from the given roots
• Last Updated : 08 Apr, 2021

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

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.`

## Javascript

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

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