Raíces de la ecuación cuadrática cuando a + b + c = 0 sin usar la fórmula de Shridharacharya

Dados tres enteros a , b y c tales que a + b + c = 0 . La tarea es encontrar las raíces de una ecuación cuadrática ax ² + bx + c = 0 .
Ejemplos: 
 

Entrada: a = 1, b = 2, c = -3 
Salida: 1, -3
Entrada: a = -5, b = 3, c = 2 
Salida: 1, -2,5 
 

Planteamiento: Cuando a + b + c = 0 entonces las raíces de la ecuación ax ² + bx + c = 0 son siempre 1 y c/a . 
Por ejemplo, 
 

Toma a = 3, b = 2 y c = -5 tal que a + b + c = 0 
Ahora, la ecuación será 3x ² + 2x – 5 = 0 
Resolviendo para x, 
3x ² + 5x – 3x – 5 = 0 
x * (3x + 5) -1 * (3x + 5) = 0 
(x – 1) * (3x + 5) = 0 
x = 1, x = (-5/3) = (c/a) 
 

A continuación se muestra la implementación del enfoque anterior: 
 

// 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 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 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# 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 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.
?>

<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>

1, -2.5

Complejidad de tiempo: O(1), solo hay aritmética básica que ocurre en tiempo constante.

Espacio Auxiliar: O(1), no se toma espacio extra.