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++

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// C++ implementation of the approach
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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PHP

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<?php
// PHP implementation of the approach
  
// Function to print the roots of the
// quadratic equation when a + b + c = 0
function printRoots($a, $b, $c)
{
    echo "1";
    echo ", ";
    echo $c / ($a * 1.0);
}
  
// Driver code
$a = 2;
$b = 3;
$c = -5;
printRoots($a, $b, $c);
  
// This code is contributed by Naman_Garg.
?>

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Output:

1, -2.5

Time Complexity: O(1)



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