find the characteristic and minimal polynomial of the matrix
$$B=\begin{pmatrix} a & 1 & 0 & 0 \\ b & 0 & 1 & 0 \\ c & 0 & 0 & 1 \\ d & 0 & 0 & 0 \end{pmatrix}$$
where $a,b,c,d$ are real numbers
I calculated the characteristic polynomial: $x^4 - ax^3 - bx^2 - cx - d$. I don't know how to go about finding the minimal polynomial
thanks for help