Given three integers A, B, and C representing the coefficients of a quadratic equation Ax2 + Bx + C = 0, the task is to find the quadratic equation whose roots are reciprocal to the roots of the given equation.
Examples:
Input: A = 1, B = -5, C = 6
Output: (6)x^2 +(-5)x + (1) = 0
Explanation:
The given quadratic equation x2 – 5x + 6 = 0.
Roots of the above equation are 2, 3.
Reciprocal of these roots are 1/2, 1/3.
Therefore, the quadratic equation with these reciprocal roots is 6x2 – 5x + 1 = 0.Input: A = 1, B = -7, C = 12
Output: (12)x^2 +(-7)x + (1) = 0
Approach: The idea is to use the concept of quadratic roots to solve the problem. Follow the steps below to solve the problem:
- Consider the roots of the equation Ax2 + Bx + C = 0 to be p, q.
- The product of the roots of the above equation is given by p * q = C / A.
- The sum of the roots of the above equation is given by p + q = -B / A.
- Therefore, the reciprocals of the roots are 1/p, 1/q.
- The product of these reciprocal roots is 1/p * 1/q = A / C.
- The sum of these reciprocal roots is 1/p + 1/q = -B / C.
- If the sum and product of roots is known, the quadratic equation can be x2 – (Sum of the roots)x + (Product of the roots) = 0.
- On solving the above equation, quadratic equation becomes Cx2 + Bx + A = 0.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the quadratic// equation having reciprocal rootsvoid findEquation(int A, int B, int C){ // Print quadratic equation cout << "(" << C << ")" << "x^2 +(" << B << ")x + (" << A << ") = 0";}// Driver Codeint main(){ // Given coefficients int A = 1, B = -5, C = 6; // Function call to find the quadratic // equation having reciprocal roots findEquation(A, B, C); return 0;} |
Java
// Java program for the above approachclass GFG{ // Function to find the quadratic// equation having reciprocal rootsstatic void findEquation(int A, int B, int C){ // Print quadratic equation System.out.print("(" + C + ")" + "x^2 +(" + B + ")x + (" + A + ") = 0");}// Driver Codepublic static void main(String args[]){ // Given coefficients int A = 1, B = -5, C = 6; // Function call to find the quadratic // equation having reciprocal roots findEquation(A, B, C);}}// This code is contributed by AnkThon |
Python3
# Python3 program for the above approach# Function to find the quadratic# equation having reciprocal rootsdef findEquation(A, B, C): # Print quadratic equation print("(" + str(C) + ")" + "x^2 +(" + str(B) + ")x + (" + str(A) + ") = 0")# Driver Codeif __name__ == "__main__": # Given coefficients A = 1 B = -5 C = 6 # Function call to find the quadratic # equation having reciprocal roots findEquation(A, B, C)# This code is contributed by AnkThon |
C#
// C# program for the above approachusing System;using System.Collections.Generic;class GFG{ // Function to find the quadratic// equation having reciprocal rootsstatic void findEquation(int A, int B, int C){ // Print quadratic equation Console.Write("(" + C + ")" + "x^2 +(" + B + ")x + (" + A + ") = 0");}// Driver Codepublic static void Main(){ // Given coefficients int A = 1, B = -5, C = 6; // Function call to find the quadratic // equation having reciprocal roots findEquation(A, B, C);}}// This code is contributed by bgangwar59 |
Javascript
<script> // Javascript program for the above approach // Function to find the quadratic // equation having reciprocal roots function findEquation(A, B, C) { // Print quadratic equation document.write("(" + C + ")" + "x^2 +(" + B + ")x + (" + A + ") = 0") } // Driver Code // Given coefficients let A = 1, B = -5, C = 6; // Function call to find the quadratic // equation having reciprocal roots findEquation(A, B, C); // This code is contributed by Hritik </script> |
Output:
(6)x^2 +(-5)x + (1) = 0
Time Complexity: O(1)
Auxiliary Space: O(1)
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