Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Check whether one root of the Quadratic Equation is twice of other or not

  • Last Updated : 23 Jun, 2021

Given three numbers A, B, C which represents the coefficients(constants) of a quadratic equation Ax^{2} + Bx + C = 0   , the task is to check whether one root of the equation represented by these constants is twice of other or not.
Examples: 
 

Input: A = 1, B = -3, C = 2 
Output: Yes 
Explanation: 
The given quadratic equation is x^{2} - 3x + 2 = 0
Its roots are (1, 2). 2 = 2 * 1
Input: A = 1, B = -5, C = 6 
Output: No 
Explanation: 
The given quadratic equation is x^{2} - 5x + 6 = 0
Its roots are (2, 3). 3 \ne 2 * 2   or 2 \ne 2 * 3
 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

 



Approach: The idea is to use the concept of quadratic roots to solve the problem. We can formulate the condition required to check whether one root is twice of the other or not by:
 

  1. The sum of roots = \alpha   2*\alpha   = 3\alpha   . This value is equal to: 
     

\frac{-b}{a}
 

  1. Similarly, the product of the roots = \alpha   2*\alpha   = 2\alpha^2   . This value is equal to: 
     

\frac{c}{a}
 

  1. We can solve the above two equations 3 * \alpha = \frac{-b}{a}   and 2 * \alpha^2 = \frac{c}{a}   to get the condition: 
     

2b^2 = 9 * a * c
 

  1. Therefore, inorder for the first assumption of the roots to hold true, the above condition needs to hold true. Hence, we simply check if the above condition is true or not for the given coefficients.

Below is the implementation of the above approach: 
 

C++




// C++ program to check if one root
// of a Quadratic Equation is
// twice of other or not
 
#include <iostream>
using namespace std;
 
// Function to find the required answer
void checkSolution(int a, int b, int c)
{
    if (2 * b * b == 9 * a * c)
        cout << "Yes";
    else
        cout << "No";
}
 
// Driver code
int main()
{
    int a = 1, b = 3, c = 2;
 
    checkSolution(a, b, c);
 
    return 0;
}


Java




// Java program to check if one root
// of a quadratic equation is
// twice of other or not
class GFG{
 
// Function to find the required answer
static void checkSolution(int a, int b, int c)
{
    if (2 * b * b == 9 * a * c)
        System.out.print("Yes");
    else
        System.out.print("No");
}
 
// Driver Code
public static void main(String[] args)
{
    int a = 1, b = 3, c = 2;
 
    checkSolution(a, b, c);
}
}
 
// This code is contributed by shubham


Python3




# Python3 program to check if one root
# of a Quadratic Equation is
# twice of other or not
 
# Function to find the required answer
def checkSolution(a, b, c):
 
    if (2 * b * b == 9 * a * c):
        print("Yes");
    else:
        print("No");
 
# Driver code
a = 1; b = 3; c = 2;
checkSolution(a, b, c);
 
# This code is contributed by Code_Mech


C#





Javascript





Output: 

Yes

 

Time Complexity: O(1)

Auxiliary Space: O(1)




My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!