Nonexcellence of multiquadratic field extensions

Let k0 be a field, chark0≠2, n 2, a,b1,…,bn k0* such that the elements are linearly independent. We show that there exists a field extension F/k0 and an anisotropic 4-dimensional form over F such that d±( )=a, the form is isotropic and the form is not defined over F.