# 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

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

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

 ` `

Output:

```1, -2.5
```

Time Complexity: O(1)

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