Given the roots of a cubic equation **A**, **B** and **C**, the task is to form the Cubic equation from the given roots.

**Note:** The given roots are integral.

**Examples:**

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.

**Approach:** Let the root of the cubic equation (**ax ^{3} + bx^{2} + cx + d = 0**) be A, B and C. Then the given cubic equation can be represents as:

ax

^{3}+ bx^{2}+ cx + d = x^{3}– (A + B + C)x^{2}+ (AB + BC +CA)x + A*B*C = 0.

Let X = (A + B + C)

Y = (AB + BC +CA)

Z = A*B*C

Therefore using the above relation find the value of **X**, **Y**, and **Z** and form the required cubic equation.

Below is the implementation of the above approach:

## C++

`// C++ program for the approach ` ` ` `#include <bits/stdc++.h> ` `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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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**Output:**

x^3 - 10x^2 + 31x - 30 = 0

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