Why is it, that for the matrix
$A \in \text{Mat}(n\times n, \mathbb{C})$
the characteristic polynomial $\chi_A(t)$ and the minimal polynomial $\mu_A(t)$ have same roots?
Since $\chi_A(t) = \mu_A(t) \cdot p(t)$ it should be easy to follow, that $\chi_A(t)$ has roots where $\mu_A(t)$ has roots.
But why can't $\chi_A(t)$ have roots where $\mu_A(t)$ hasn't?