Why is $\mathbb{Q}_p\langle T\rangle/\mathfrak{m}$ a finite extension of $\mathbb{Q}_p$

Question

$\mathbb{Q}_p\langle T\rangle$ is the Tate algebra, which, by definition, is the $\mathbb{Q}_p$-algebra of power series in $\mathbb{Q}_p[[T]]$ whose coefficients tend to zero. Let $\mathfrak{m}$ be a maximal ideal of $\mathbb{Q}_p\langle T\rangle$. How can you show that $\mathbb{Q}_p\langle T\rangle /\mathfrak{m}$ is a finite extension of $\mathbb{Q}_p$?