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Roots of the quadratic equation when a + b + c = 0 without using Shridharacharya formula
  • Difficulty Level : Medium
  • Last Updated : 26 Mar, 2021
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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 <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;
}

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




<?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.
?>

Javascript




<script>
// Javascript implementation of the approach
 
// Function to print the roots of the
// quadratic equation when a + b + c = 0
function printRoots(a, b, c)
{
    document.write(1 + ", " + c / (a * 1.0));
}
 
// Driver code
var a = 2;
var b = 3;
var c = -5;
printRoots(a, b, c);
 
// This code is contributed by noob2000.
</script>
Output: 
1, -2.5

 

Time Complexity: O(1)
 

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