Ruffini's theroem for polynomial in c++

Question

I need help in order to do a program that solve polynomials with ruffini theorem

Answer 1

I'm not a mathematician. I am not familiar with the Ruffini Theorem.

After a quick search, this is what I found: https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

The Ruffini Theorem states that

there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients.

Based on this it is not clear how you want to use this theorem to help you solve polynomials.

Could you please elaborate?

Or are you simply after a program that calculates the solution of a quadratic equation?

Answer 2

I guess you mean Ruffini's Rule.
It's also called Briot-Ruffini algorithm.

What it does?

The algorithm consists in reduce a polynomial degree in 1 unit, dividing a polynomial expression by a (x-x₀) in the following way:

First, let the polynomial expression be f(x) = a₁xⁿ + a₂x^n-1+ ... + a_n-1x² + a_nx¹.

x₀ | a₁  a₂  a₃ ... a_n-1  a_n
___________________
      a₁  b    c   ...  z     0   

Note that the first coefficient under a₁ is also a₁ and the one under a_n is 0.

the values of a₁, b, c, ..., z will be the coefficients of the reduced  polynomial, g(x) = a₁x^n-1 + bx^n-2+ ... + yx² + zx¹, due to f(x) = g(x) * (x-x₀).

The coefficients of g(x), (b, c, ..., y and z) are calculated by multiplying the number at it's left side for x₀, then sum it with the number above it. See the following way:
b = a₁ * x₀ + a₂
c = b * x₀ + a₃
d = c * x₀ + a₄
...
z = y * x₀ + a_n-1