Is $K(X)$ never algebraically closed?

454 Views Asked by At

I saw an exercise like this:

Let $K$ be a algebraically closed field. Show that $K(X)$ is not algebraically closed.

I was trying to prove that $T^2-X$ has not root in $K(X)$. How do I show it? Does it really use the hypothesis about $K$?

Thank you!