I have a polynomial equation, from which we need to approximate the value of $r$, the equation is like
$C_0r^n -C_1r^{n-1}+C_3r^{n-2}-C_4r^{n-3}...-C_{n-1}r+C=0$
Is there a way to approximate the value of $r$ by "computing the eigenvalues of a companion matrix", I know very little about linear algebra, can anyone plz guide me how to go about doing this.
First, this is NOT an "equation" because there is no "="! It is simply a polynomial.
Second, Do you know what a "companion matrix" is? According to Wolfram (https://mathworld.wolfram.com/CompanionMatrix.html) the companion matrix to the polynomial $C_0r^n- C_1r^{n-1}+ C_2r^{n-2}+ \cdot\cdot\cdot+ C_{n-1}r+ C_n$ is $\begin{bmatrix}0 & 0 & \cdot\cdot\cdot C_0 \\ 0 & 0 & \cdot\cdot\cdot C_1 \\0 & 0 & \cdot\cdot\cdot C_2 \\ \cdot \\\cdot\\\cdot \\ 0 & 0 & \cdot\cdot\cdot C_{n-1} \\ 0 & 0 & \cdot\cdot\cdot C_n\end{bmatrix}$