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

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

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:



    Let the roots of the given quadratic equation be \alpha and 2*\alpha.

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

    \frac{-b}{a}

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

    \frac{c}{a}

  3. 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

  4. 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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// C# program to check if one root 
// of a quadratic equation is 
// twice of other or not 
using System;
class GFG{ 
  
// Function to find the required answer 
static void checkSolution(int a, int b, int c) 
    if (2 * b * b == 9 * a * c) 
        Console.WriteLine("Yes"); 
    else
        Console.WriteLine("No"); 
  
// Driver Code 
public static void Main()
    int a = 1, b = 3, c = 2; 
  
    checkSolution(a, b, c); 
  
// This code is contributed by shivanisinghss2110

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Output:

Yes

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