给定三次方程式A , B和C的根,任务是从给定的根形成三次方程式。
注意:给定的根是整数。
例子:
Input: A = 1, B = 2, C = 3
Output: x^3 – 6x^2 + 11x – 6 = 0
Explanation:
Since 1, 2, and 3 are roots of the cubic equations, Then equation is given by:
(x – 1)(x – 2)(x – 3) = 0
(x – 1)(x^2 – 5x + 6) = 0
x^3 – 5x^2 + 6x – x^2 + 5x – 6 = 0
x^3 – 6x^2 + 11x – 6 = 0.
Input: A = 5, B = 2, C = 3
Output: x^3 – 10x^2 + 31x – 30 = 0
Explanation:
Since 5, 2, and 3 are roots of the cubic equations, Then equation is given by:
(x – 5)(x – 2)(x – 3) = 0
(x – 5)(x^2 – 5x + 6) = 0
x^3 – 5x^2 + 6x – 5x^2 + 25x – 30 = 0
x^3 – 10x^2 + 31x – 30 = 0.
方法:令三次方程的根( ax 3 + bx 2 + cx + d = 0 )为A,B和C。则给定的三次方程可表示为:
ax3 + bx2 + cx + d = x3 – (A + B + C)x2 + (AB + BC +CA)x + A*B*C = 0.
Let X = (A + B + C)
Y = (AB + BC +CA)
Z = A*B*C
因此,使用上述关系式找到X , Y和Z的值,并形成所需的三次方程。
下面是上述方法的实现:
C++
// C++ program for the approach
#include
using namespace std;
// Function to find the cubic
// equation whose roots are a, b and c
void findEquation(int a, int b, int c)
{
// Find the value of coefficient
int X = (a + b + c);
int Y = (a * b) + (b * c) + (c * a);
int Z = a * b * c;
// Print the equation as per the
// above coefficients
cout << "x^3 - " << X << "x^2 + "
<< Y << "x - " << Z << " = 0";
}
// Driver Code
int main()
{
int a = 5, b = 2, c = 3;
// Function Call
findEquation(a, b, c);
return 0;
}
Java
// Java program for the approach
class GFG{
// Function to find the cubic equation
// whose roots are a, b and c
static void findEquation(int a, int b, int c)
{
// Find the value of coefficient
int X = (a + b + c);
int Y = (a * b) + (b * c) + (c * a);
int Z = a * b * c;
// Print the equation as per the
// above coefficients
System.out.print("x^3 - " + X+ "x^2 + "
+ Y+ "x - " + Z+ " = 0");
}
// Driver Code
public static void main(String[] args)
{
int a = 5, b = 2, c = 3;
// Function Call
findEquation(a, b, c);
}
}
// This code contributed by PrinciRaj1992
Python3
# Python3 program for the approach
# Function to find the cubic equation
# whose roots are a, b and c
def findEquation(a, b, c):
# Find the value of coefficient
X = (a + b + c);
Y = (a * b) + (b * c) + (c * a);
Z = (a * b * c);
# Print the equation as per the
# above coefficients
print("x^3 - " , X ,
"x^2 + " ,Y ,
"x - " , Z , " = 0");
# Driver Code
if __name__ == '__main__':
a = 5;
b = 2;
c = 3;
# Function Call
findEquation(a, b, c);
# This code is contributed by sapnasingh4991
C#
// C# program for the approach
using System;
class GFG{
// Function to find the cubic equation
// whose roots are a, b and c
static void findEquation(int a, int b, int c)
{
// Find the value of coefficient
int X = (a + b + c);
int Y = (a * b) + (b * c) + (c * a);
int Z = a * b * c;
// Print the equation as per the
// above coefficients
Console.Write("x^3 - " + X +
"x^2 + " + Y +
"x - " + Z + " = 0");
}
// Driver Code
public static void Main()
{
int a = 5, b = 2, c = 3;
// Function Call
findEquation(a, b, c);
}
}
// This code is contributed by shivanisinghss2110
Javascript
x^3 - 10x^2 + 31x - 30 = 0