Given three numbers A, B, C which represents the coefficients(constants) of a quadratic equation 
, the task is to check whether the roots of the equation represented by these constants are reciprocal of each other or not.
Examples:
Input: A = 2, B = -5, C = 2
Output: Yes
Explanation:
The given quadratic equation is.
Its roots are (1, 1/1) which are reciprocal of each other.
Input: A = 1, B = -5, C = 6
Output: No
Explanation:
The given quadratic equation is.
Its roots are (2, 3) which are not reciprocal of each other.
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 the reciprocal of the other or not by:
- Let the roots of the equation be
and 
. - The product of the roots of the above equation is given by * .
- It is known that the product of the roots is C/A. Therefore, the required condition is C = A.
Below is the implementation of the above approach:
C++
// C++ program to check if roots// of a Quadratic Equation are// reciprocal of each other or not#include <iostream>using namespace std;// Function to check if the roots // of a quadratic equation are// reciprocal of each other or notvoid checkSolution(int a, int b, int c){ if (a == c) cout << "Yes"; else cout << "No";}// Driver codeint main(){ int a = 2, b = 0, c = 2; checkSolution(a, b, c); return 0;} |
Java
// Java program to check if roots // of a quadratic equation are // reciprocal of each other or not class GFG{ // Function to check if the roots // of a quadratic equation are // reciprocal of each other or not static void checkSolution(int a, int b, int c) { if (a == c) System.out.print("Yes"); else System.out.print("No"); } // Driver code public static void main(String[] args) { int a = 2, b = 0, c = 2; checkSolution(a, b, c); } } // This code is contributed by shubham |
Python3
# Python3 program to check if roots# of a Quadratic Equation are# reciprocal of each other or not# Function to check if the roots # of a quadratic equation are# reciprocal of each other or notdef checkSolution(a, b, c): if (a == c): print("Yes"); else: print("No");# Driver codea = 2; b = 0; c = 2;checkSolution(a, b, c);# This code is contributed by Code_Mech |
C#
// C# program to check if roots // of a quadratic equation are // reciprocal of each other or not using System;class GFG{// Function to check if the roots // of a quadratic equation are // reciprocal of each other or not static void checkSolution(int a, int b, int c) { if (a == c) Console.WriteLine("Yes"); else Console.WriteLine("No"); } // Driver code public static void Main(){ int a = 2, b = 0, c = 2; checkSolution(a, b, c); } } // This code is contributed by shivanisinghss2110 |
Javascript
<script> // Javascript program to check if roots // of a Quadratic Equation are // reciprocal of each other or not // Function to check if the roots // of a quadratic equation are // reciprocal of each other or not function checkSolution(a, b, c) { if (a == c) document.write("Yes"); else document.write("No"); } let a = 2, b = 0, c = 2; checkSolution(a, b, c); </script> |
Yes
Time Complexity: O(1)
Auxiliary Space: O(1)
Using Quadratic Formula in python:
We can find the roots of a quadratic equation using the quadratic formula:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
If the roots are reciprocal of each other, then one of the roots is the reciprocal of the other:
x1 * x2 = 1
x2 = 1 / x1
Substituting x2 in terms of x1 in the above quadratic formula:
x1 = (-b ± sqrt(b^2 – 4ac)) / 2a
1 / x1 = (-b ? sqrt(b^2 – 4ac)) / 2a
So, we can find the roots using the quadratic formula and check if they satisfy the above condition to be reciprocal of each other.
- Calculate the discriminant of the quadratic equation using the formula discriminant = B**2 – 4*A*C.
- If the discriminant is negative, return False as the quadratic equation has no real roots.
- Calculate the roots of the quadratic equation using the formula root1 = (-B + math.sqrt(discriminant)) / (2*A) and root2 = (-B – math.sqrt(discriminant)) / (2*A).
- Check if the product of the roots root1 * root2 is equal to 1.
- If the product is equal to 1, return True as the roots are reciprocal of each other. Otherwise, return False.
C++
#include <iostream>#include <cmath>// Function to check if roots are reciprocal of each otherbool areRootsReciprocal(double A, double B, double C) { // Calculate the discriminant double discriminant = B * B - 4 * A * C; // If discriminant is negative, roots are imaginary if (discriminant < 0) { return false; } // Calculate the roots double root1 = (-B + sqrt(discriminant)) / (2 * A); double root2 = (-B - sqrt(discriminant)) / (2 * A); // Check if the product of roots is equal to 1 return root1 * root2 == 1;}int main() { // Example inputs double A1 = 2, B1 = -5, C1 = 2; double A2 = 1, B2 = -5, C2 = 6; // Check if roots are reciprocal for the first set of coefficients if (areRootsReciprocal(A1, B1, C1)) { std::cout << "Yes" << std::endl; } else { std::cout << "No" << std::endl; } // Check if roots are reciprocal for the second set of coefficients if (areRootsReciprocal(A2, B2, C2)) { std::cout << "Yes" << std::endl; } else { std::cout << "No" << std::endl; } return 0;} |
Python3
import mathdef are_roots_reciprocal(A, B, C): discriminant = B**2 - 4*A*C if discriminant < 0: return False root1 = (-B + math.sqrt(discriminant)) / (2*A) root2 = (-B - math.sqrt(discriminant)) / (2*A) return root1 * root2 == 1# Example inputsA1, B1, C1 = 2, -5, 2A2, B2, C2 = 1, -5, 6# Check if roots are reciprocal of each otherif are_roots_reciprocal(A1, B1, C1): print("Yes")else: print("No")if are_roots_reciprocal(A2, B2, C2): print("Yes")else: print("No") |
Javascript
function areRootsReciprocal(A, B, C) { let discriminant = B ** 2 - 4 * A * C; if (discriminant < 0) { return false; } let root1 = (-B + Math.sqrt(discriminant)) / (2 * A); let root2 = (-B - Math.sqrt(discriminant)) / (2 * A); return root1 * root2 === 1;}// Example inputslet A1 = 2, B1 = -5, C1 = 2;let A2 = 1, B2 = -5, C2 = 6;// Check if roots are reciprocal of each otherif (areRootsReciprocal(A1, B1, C1)) { console.log("Yes");} else { console.log("No");}if (areRootsReciprocal(A2, B2, C2)) { console.log("Yes");} else { console.log("No");} |
Yes No
Time Complexity: O(1)
Space Complexity: O(1)
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