The algebraic closure in function fields of quadratic forms in characteristic 2

For a field k of characteristic not two, it is known that k is algebraically closed in the function field of any (non-degenerate) quadratic form in three or more variables. In this note we consider fields of characteristic two and decide when k is algebraically closed in a function field of a quadratic k -form. For quadratic forms in three variables this has recently been done by Ohm.