Quotient of Ring of Functions on a Field by a Maximal Ideal is Algebraically Closed Implies Field is Algebraically Closed

Question

I'm having trouble with this one.

Let $K$ be a field, $X$ a non-empty set, and $\mathcal{F}(X;K)$ the ring of functions from X on K. If $\mathfrak{m}$ is a maximal ideal of $\mathcal{F}(X;K)$ such that $\mathcal{F}(X;K)/ \mathfrak{m}$ is an algebraically closed field, then $K$ is algebraically closed too.

I don't know where to start. Any hints?