# Quadratic equation whose roots are K times the roots of given equation

• Last Updated : 13 May, 2021

Given three integers A, B, and C representing the coefficients of a quadratic equation Ax2 + Bx + C = 0 and a positive integer K, the task is to find the coefficients of the quadratic equation whose roots are K times the roots of the given equation.

Examples:

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

Input: A = 1, B = 2, C = 1, K = 2
Output: 1 4 4
Explanation:
The given quadratic equation x2 + 2x + 1 = 0.
Roots of the above equation are -1, -1.
Double of these roots are -2, -2.
Therefore, the quadratic equation with the roots (-2, -2) is x2 + 4x + 4 = 0.

Input: A = 1, B = -7, C = 12, K = 2
Output: 1 -14 48

Approach: The given problem can be solved by using the concept of quadratic roots. Follow the steps below to solve the problem:

• Let the roots of the equation Ax2 + Bx + C = 0 be P and Q respectively.
• Then, the product of the roots of the above equation is given by P * Q = C / A and the sum of the roots of the above equation is given by P + Q = -B / A.
• Therefore, the product of the roots of the required equation is equal to:

(K * P ) * (K * Q) = K2 * P * Q = (K2 * C ) / A

• Similarly, the sum of the roots of the required equation is 2 * K (-B / C).
• Therefore, the required quadratic equation is equal to:

x2 – (Sum of the roots)x + (Product of the roots) = 0

=> Ax2 + (KB)x + (K2)C = 0

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Function to find the quadratic` `// equation whose roots are K times` `// the roots of the given equation` `void` `findEquation(``int` `A, ``int` `B, ``int` `C,` `                  ``int` `K)` `{` `    ``// Print quadratic equation` `    ``cout << A << ``" "` `<< K * B` `         ``<< ``" "` `<< K * K * C;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `A = 1, B = 2, C = 1, K = 2;`   `    ``findEquation(A, B, C, K);`   `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `import` `java.util.*;`   `class` `GFG{`   `// Function to find the quadratic` `// equation whose roots are K times` `// the roots of the given equation` `static` `void` `findEquation(``int` `A, ``int` `B, ` `                         ``int` `C, ``int` `K)` `{` `    `  `    ``// Print quadratic equation` `    ``System.out.print(A + ``" "` `+ K * B + ` `                      ``" "` `+ K * K * C);` `}`   `// Driver Code` `public` `static` `void` `main(String []args)` `{` `    ``int` `A = ``1``, B = ``2``, C = ``1``, K = ``2``;`   `    ``findEquation(A, B, C, K);` `}` `}`

## Python3

 `# Python3 program for the above approach`   `# Function to find the quadratic` `# equation whose roots are K times` `# the roots of the given equation` `def` `findEquation(A, B, C, K):` `  `  `    ``# Prquadratic equation` `    ``print``(A, K``*``B, K``*``K``*``C)`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``A, B, C, K ``=` `1``, ``2``, ``1``, ``2`   `    ``findEquation(A, B, C, K)`   `# This code is contributed by mohit kumar 29.`

## C#

 `// C# program for the above approach` `using` `System;`   `class` `GFG{`   `// Function to find the quadratic` `// equation whose roots are K times` `// the roots of the given equation` `static` `void` `findEquation(``int` `A, ``int` `B, ` `                         ``int` `C, ``int` `K)` `{` `    `  `    ``// Print quadratic equation` `    ``Console.Write(A + ``" "` `+ K * B + ` `                      ``" "` `+ K * K * C);` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `    ``int` `A = 1, B = 2, C = 1, K = 2;`   `    ``findEquation(A, B, C, K);` `}` `}` `    `  `// This code is contributed by ukasp`

## Javascript

 ``

Output:

`1 4 4`

Time Complexity: O(1)
Auxiliary Space: O(1)

My Personal Notes arrow_drop_up
Recommended Articles
Page :