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Find the quadratic equation from the given roots
  • Last Updated : 08 Apr, 2021

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++




// 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;
}

Java




// 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

Python3




# 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

C#




// 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.

Javascript




<script>
 
// Javascript implementation of the above approach
 
// Function to find the quadratic
// equation whose roots are a and b
function findEquation(a, b)
{
    var sum = (a + b);
    var product = (a * b);
    document.write("x^2 - (" + sum +
                    "x) + (" + product +
                    ") = 0");
}
 
// Driver Code
var a = 2, b = 3;
 
findEquation(a, b);
 
// This code is contributed by Ankita saini
     
</script>
Output: 
x^2 - (5x) + (6) = 0

 

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