Forme la ecuación cúbica a partir de las raíces dadas

Dadas las raíces de una ecuación cúbica A , B y C , la tarea es formar la ecuación cúbica a partir de las raíces dadas.
Nota: Las raíces dadas son integrales.
Ejemplos: 
 

Entrada: A = 1, B = 2, C = 3 
Salida: x^3 – 6x^2 + 11x – 6 = 0 
Explicación: 
Dado que 1, 2 y 3 son raíces de las ecuaciones cúbicas, la ecuación viene dada por: 
(x – 1)(x – 2)(x – 3) = 0 
(x – 1)(x^2 – 5x + 6) = 0 
x^3 – 5x^2 + 6x – x^2 + 5x – 6 = 0 
x^3 – 6x^2 + 11x – 6 = 0.
Entrada: A = 5, B = 2, C = 3 
Salida: x^3 – 10x^2 + 31x – 30 = 0 
Explicación: 
Dado que 5, 2 , y 3 son raíces de las ecuaciones cúbicas. Entonces, la ecuación viene dada por: 
(x – 5)(x – 2)(x – 3) = 0 
(x – 5)(x^2 – 5x + 6) = 0 
x ^3 – 5x^2 + 6x – 5x^2 + 25x – 30 = 0 
x^3 – 10x^2 + 31x – 30 = 0. 
 

Enfoque: Deje que la raíz de la ecuación cúbica ( ax ³ + bx ² + cx + d = 0 ) sea A, B y C. Luego, la ecuación cúbica dada se puede representar como: 
 

ax ³ + bx ² + cx + d = x ³ – (A + B + C)x ² + (AB + BC+CA)x + A*B*C = 0. 
Sea X = (A + B + C) 
Y = (AB + BC+CA) 
Z = A*B*C 
 

Por lo tanto, utilizando la relación anterior, encuentre el valor de X , Y y Z y forme la ecuación cúbica requerida.
A continuación se muestra la implementación del enfoque anterior:
 

// C++ program for the approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the cubic
// equation whose roots are a, b and c
void findEquation(int a, int b, int c)
{
    // Find the value of coefficient
    int X = (a + b + c);
    int Y = (a * b) + (b * c) + (c * a);
    int Z = a * b * c;
 
    // Print the equation as per the
    // above coefficients
    cout << "x^3 - " << X << "x^2 + "
         << Y << "x - " << Z << " = 0";
}
 
// Driver Code
int main()
{
    int a = 5, b = 2, c = 3;
 
    // Function Call
    findEquation(a, b, c);
    return 0;
}

// Java program for the approach
 
class GFG{
 
// Function to find the cubic equation
// whose roots are a, b and c
static void findEquation(int a, int b, int c)
{
    // Find the value of coefficient
    int X = (a + b + c);
    int Y = (a * b) + (b * c) + (c * a);
    int Z = a * b * c;
 
    // Print the equation as per the
    // above coefficients
    System.out.print("x^3 - " + X+ "x^2 + "
                  + Y+ "x - " + Z+ " = 0");
}
 
// Driver Code
public static void main(String[] args)
{
    int a = 5, b = 2, c = 3;
 
    // Function Call
    findEquation(a, b, c);
}
}
 
// This code contributed by PrinciRaj1992

# Python3 program for the approach
 
# Function to find the cubic equation
# whose roots are a, b and c
def findEquation(a, b, c):
     
    # Find the value of coefficient
    X = (a + b + c);
    Y = (a * b) + (b * c) + (c * a);
    Z = (a * b * c);
 
    # Print the equation as per the
    # above coefficients
    print("x^3 - " , X ,
          "x^2 + " ,Y ,
          "x - " , Z , " = 0");
 
# Driver Code
if __name__ == '__main__':
     
    a = 5;
    b = 2;
    c = 3;
 
    # Function Call
    findEquation(a, b, c);
 
# This code is contributed by sapnasingh4991

// C# program for the approach
using System;
 
class GFG{
 
// Function to find the cubic equation
// whose roots are a, b and c
static void findEquation(int a, int b, int c)
{
     
    // Find the value of coefficient
    int X = (a + b + c);
    int Y = (a * b) + (b * c) + (c * a);
    int Z = a * b * c;
 
    // Print the equation as per the
    // above coefficients
    Console.Write("x^3 - " + X +
                  "x^2 + " + Y +
                    "x - " + Z + " = 0");
}
 
// Driver Code
public static void Main()
{
    int a = 5, b = 2, c = 3;
 
    // Function Call
    findEquation(a, b, c);
}
}
 
// This code is contributed by shivanisinghss2110

<script>
 
    // Javascript program for the approach
     
    // Function to find the cubic
    // equation whose roots are a, b and c
    function findEquation(a, b, c)
    {
        // Find the value of coefficient
        let X = (a + b + c);
        let Y = (a * b) + (b * c) + (c * a);
        let Z = a * b * c;
 
        // Print the equation as per the
        // above coefficients
        document.write("x^3 - " + X + "x^2 + "
             + Y + "x - " + Z + " = 0");
    }
       
    let a = 5, b = 2, c = 3;
   
    // Function Call
    findEquation(a, b, c);
 
</script>

x^3 - 10x^2 + 31x - 30 = 0

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