二次方程的根是给定方程的根的 K 倍

给定三个整数A 、 B和C代表二次方程Ax ² + Bx + C = 0的系数和一个正整数K ，任务是找到二次方程的系数，其根是二次方程的根的K 倍给定的方程。

例子：

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

方法：给定的问题可以通过使用二次根的概念来解决。请按照以下步骤解决问题：

• 设方程Ax ² + Bx + C = 0的根分别为P和Q。
• 然后，上述方程的根的乘积由P * Q = C / A给出，上述方程的根之和由P + Q = -B / A 给出。
• 因此，所需方程的根的乘积等于：

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

• 同样，所需方程的根之和为2 * K (-B / C) 。
• 因此，所需的二次方程等于：

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

=> Ax² + (KB)x + (K²)C = 0

下面是上述方法的实现：

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

// 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.

输出：

1 4 4

时间复杂度： O(1)
辅助空间： O(1)