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Find if two given Quadratic equations have common roots or not
• Last Updated : 17 Mar, 2021

Given values a1, b1 and c1 of first Quadratic equations and values a2, b2 and c2 of second Quadratic equations , the task is to find whether both quadratic equations have common roots or not.
Examples:

Input: a1 = 1, b1 = -5, c1 = 6, a2 = 2, b2 = -10, c2 = 12
Output: Yes
Explanation:
Roots of both quadratic equations are (2, 3)
Input: a1 = 1, b1 = -5, c1 = 6, a2 = 1, b2 = -9, c2 = 20
Output: No
Explanation:
Roots of first quadratic equations are (2, 3), and Roots of second quadratic equations are (4, 5)
Therefore, both quadratic equations have differnt roots.

Approach:
Let the two quadratic equations are and

• Let us assume the given condition to be true, i.e. both the equations have common roots, say and

• As we know that
and
where a, b, c represents the quadratic equation

• Therefore,

• Now since both the roots are common,
Therfore, from above equations

• Also,

• Combining the above equations:

• which is the required condition for both roots to be common of the two quadratic equations.

Programs:

## C++

 // C++ Program to Find if two given// Quadratic equations have// common roots or not #include using namespace std; // function to check if 2 quadratic// equations have common roots or not.bool checkSolution(float a1, float b1,                   float c1, float a2,                   float b2, float c2){    return (a1 / a2) == (b1 / b2)           && (b1 / b2) == (c1 / c2);} // Driver codeint main(){    float a1 = 1, b1 = -5, c1 = 6;    float a2 = 2, b2 = -10, c2 = 12;    if (checkSolution(a1, b1, c1, a2, b2, c2))        cout << "Yes";    else        cout << "No";    return 0;}

## Java

 // Java Program to Find if two given// quadratic equations have common// roots or notclass GFG {     // Function to check if 2 quadratic// equations have common roots or not.static boolean checkSolution(float a1, float b1,                             float c1, float a2,                             float b2, float c2){    return ((a1 / a2) == (b1 / b2) &&            (b1 / b2) == (c1 / c2));}     // Driver codepublic static void main (String[] args){    float a1 = 1, b1 = -5, c1 = 6;    float a2 = 2, b2 = -10, c2 = 12;             if (checkSolution(a1, b1, c1, a2, b2, c2))        System.out.println("Yes");    else        System.out.println("No");}} // This code is contributed by AnkitRai01

## Python3

 # Python3 program to find if two given# quadratic equations have common # roots or not # Function to check if 2 quadratic# equations have common roots or not.def checkSolution(a1, b1, c1, a2, b2, c2):         return ((a1 / a2) == (b1 / b2) and            (b1 / b2) == (c1 / c2)) # Driver codea1, b1, c1 = 1, -5, 6a2, b2, c2 = 2, -10, 12 if (checkSolution(a1, b1, c1, a2, b2, c2)):    print("Yes")else:    print("No") # This code is contributed by divyamohan123

## C#

 // C# Program to Find if two given// quadratic equations have common// roots or notusing System;class GFG{     // Function to check if 2 quadratic// equations have common roots or not.static bool checkSolution(float a1, float b1,                          float c1, float a2,                          float b2, float c2){    return ((a1 / a2) == (b1 / b2) &&            (b1 / b2) == (c1 / c2));}     // Driver codepublic static void Main (string[] args){    float a1 = 1, b1 = -5, c1 = 6;    float a2 = 2, b2 = -10, c2 = 12;             if (checkSolution(a1, b1, c1, a2, b2, c2))        Console.WriteLine("Yes");    else        Console.WriteLine("No");}} // This code is contributed by AnkitRai01

## Javascript

 
Output:
Yes

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