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# Roots of the quadratic equation when a + b + c = 0 without using Shridharacharya formula

Given three integers a, b and c such that a + b + c = 0. The task is to find the roots of a quadratic equation ax2 + bx + c = 0.
Examples:

Input: a = 1, b = 2, c = -3
Output: 1, -3
Input: a = -5, b = 3, c = 2
Output: 1, -2.5

Approach: When a + b + c = 0 then the roots of the equation ax2 + bx + c = 0 are always 1 and c / a
For example,

Take a = 3, b = 2 and c = -5 such that a + b + c = 0
Now, the equation will be 3x2 + 2x – 5 = 0
Solving for x,
3x2 + 5x – 3x – 5 = 0
x * (3x + 5) -1 * (3x + 5) = 0
(x – 1) * (3x + 5) = 0
x = 1, x = (-5 / 3) = (c / a)

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to print the roots of the``// quadratic equation when a + b + c = 0``void` `printRoots(``long` `a, ``long` `b, ``long` `c)``{``    ``cout << 1 << ``", "` `<< c / (a * 1.0);``}` `// Driver code``int` `main()``{``    ``long` `a = 2;``    ``long` `b = 3;``    ``long` `c = -5;``    ``printRoots(a, b, c);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{``    ` `    ``// Function to print the roots of the``    ``// quadratic equation when a + b + c = 0``    ``static` `void` `printRoots(``long` `a, ``long` `b, ``long` `c)``    ``{``        ``System.out.println(``1` `+ ``", "` `+ c / (a * ``1.0``));``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``long` `a = ``2``;``        ``long` `b = ``3``;``        ``long` `c = -``5``;``        ``printRoots(a, b, c);``    ``}``}` `// This code is contributed by``// sanjeev2552`

## Python3

 `# Python3 implementation of the approach` `# Function to print the roots of the``# quadratic equation when a + b + c = 0``def` `printRoots(a, b, c):``    ``print``(``1``, ``","``, c ``/` `(a ``*` `1.0``))` `# Driver code``a ``=` `2``b ``=` `3``c ``=` `-``5``printRoots(a, b, c)` `# This code is contributed by Mohit Kumar`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Function to print the roots of the``// quadratic equation when a + b + c = 0``static` `void` `printRoots(``long` `a, ``long` `b, ``long` `c)``{``    ``Console.WriteLine(``"1, "` `+ c / (a * 1.0));``}` `// Driver code``public` `static` `void` `Main()``{``    ``long` `a = 2;``    ``long` `b = 3;``    ``long` `c = -5;``    ``printRoots(a, b, c);``}``}` `// This code is contributed by Nidhi`

## PHP

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## Javascript

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Output:

`1, -2.5`

Time Complexity: O(1), there is only basic arithmetic that happens in constant time.

Auxiliary Space: O(1), no extra space is taken.

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