Solving quadratic equations over polynomial rings of characteristic two

We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation an tn + ··· + a0 = 0 with coefficients ai in A, our problem is to find its roots in A. We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1,... ,xN ] or F(x1,... ,xN ) for any finite field F and any number N of variables. The case of quadratic equations in characteristic two is studied in detail