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Find the quadratic equation from the given roots
  • Last Updated : 18 Oct, 2019

Given the roots of a quadratic equation A and B, the task is to find the equation.

Note: The given roots are integral.

Examples:

Input: A = 2, B = 3
Output: x^2 – (5x) + (6) = 0
x2 – 5x + 6 = 0
x2 -3x -2x + 6 = 0
x(x – 3) – 2(x – 3) = 0
(x – 3) (x – 2) = 0
x = 2, 3

Input: A = 5, B = 10
Output: x^2 – (15x) + (50) = 0



Approach: If the roots of a quadratic equation ax2 + bx + c = 0 are A and B then it known that
A + B = – b * a and A * B = c * a.
Now, ax2 + bx + c = 0 can be written as
x2 + (b / a)x + (c / a) = 0 (Since, a != 0)
x2 – (A + B)x + (A * B) = 0, [Since, A + B = -b * a and A * B = c * a]
i.e. x2 – (Sum of the roots)x + Product of the roots = 0

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 find the quadratic
// equation whose roots are a and b
void findEquation(int a, int b)
{
    int sum = (a + b);
    int product = (a * b);
    cout << "x^2 - (" << sum << "x) + ("
         << product << ") = 0";
}
  
// Driver code
int main()
{
    int a = 2, b = 3;
  
    findEquation(a, b);
  
    return 0;
}

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Java

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// Java implementation of the above approach 
class GFG 
{
      
    // Function to find the quadratic 
    // equation whose roots are a and b 
    static void findEquation(int a, int b) 
    
        int sum = (a + b); 
        int product = (a * b); 
        System.out.println("x^2 - (" + sum + 
                           "x) + (" + product + ") = 0"); 
    
      
    // Driver code 
    public static void main(String args[])
    
        int a = 2, b = 3
      
        findEquation(a, b); 
    
}
  
// This code is contributed by AnkitRai01

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Python3

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# Python3 implementation of the approach
  
# Function to find the quadratic
# equation whose roots are a and b
def findEquation(a, b):
    summ = (a + b)
    product = (a * b)
    print("x^2 - (", summ, 
          "x) + (", product, ") = 0")
  
# Driver code
a = 2
b = 3
  
findEquation(a, b)
  
# This code is contributed by Mohit Kumar

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C#

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// C# implementation of the above approach 
using System;
class GFG 
{
      
    // Function to find the quadratic 
    // equation whose roots are a and b 
    static void findEquation(int a, int b) 
    
        int sum = (a + b); 
        int product = (a * b); 
        Console.WriteLine("x^2 - (" + sum + 
                          "x) + (" + product + ") = 0"); 
    
      
    // Driver code 
    public static void Main()
    
        int a = 2, b = 3; 
      
        findEquation(a, b); 
    
}
  
// This code is contributed by CodeMech.

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Output:

x^2 - (5x) + (6) = 0

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