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

Given three integers **A**, **B**, and **C **representing the coefficients of a quadratic equation **Ax ^{2} + 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:**

Input:A = 1, B = 2, C = 1, K = 2Output:1 4 4Explanation:

The given quadratic equation x^{2}+ 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 x^{2}+ 4x + 4 = 0.

Input:A = 1, B = -7, C = 12, K = 2Output: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
**Ax**be^{2}+ Bx + C = 0**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) = K^{2}* P * Q = (K^{2}* 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:

x^{2}– (Sum of the roots)x + (Product of the roots) = 0

=> Ax^{2}+ (KB)x + (K^{2})C = 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 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

`<script>` `// Javascript program for the above approach` `// Function to find the quadratic` `// equation whose roots are K times` `// the roots of the given equation` `function` `findEquation(A, B, C, K)` `{` ` ` `// Print quadratic equation` ` ` `document.write( A + ` `" "` `+ K * B` ` ` `+ ` `" "` `+ K * K * C);` `}` `// Driver Code` `var` `A = 1, B = 2, C = 1, K = 2;` `findEquation(A, B, C, K);` `// This code is contributed by noob2000.` `</script>` |

**Output:**

1 4 4

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