# Form the Cubic equation from the given roots

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 = 3Output:x^3 – 6x^2 + 11x – 6 = 0Explanation:

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 = 3Output:x^3 – 10x^2 + 31x – 30 = 0Explanation:

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;` `}` |

## 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

`<script>` ` ` `// Javascript program for the approach` ` ` ` ` `// Function to find the cubic` ` ` `// equation whose roots are a, b and c` ` ` `function` `findEquation(a, b, c)` ` ` `{` ` ` `// Find the value of coefficient` ` ` `let X = (a + b + c);` ` ` `let Y = (a * b) + (b * c) + (c * a);` ` ` `let Z = a * b * c;` ` ` `// Print the equation as per the` ` ` `// above coefficients` ` ` `document.write(` `"x^3 - "` `+ X + ` `"x^2 + "` ` ` `+ Y + ` `"x - "` `+ Z + ` `" = 0"` `);` ` ` `}` ` ` ` ` `let a = 5, b = 2, c = 3;` ` ` ` ` `// Function Call` ` ` `findEquation(a, b, c);` `</script>` |

**Output:**

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

Time Complexity: O(1)

Auxiliary Space: O(1)