to every genus-2 curve c over a finite field $f_q$, one can associate the characteristic polynomials of the frobenius endomorphism acting on the jacobian of c. this polynomial --- also known as the *weil polynomial* of c --- is of the form $$x^4 + a*x^3 + b*x^2 + a*q*x + q^2$$ where a and b are integers. we will use the brauer relations, applied to a certain biquadratic number field, to show that no curve over $f_q$ gives rise to the weil polynomial with $a = 0$ and $b = 2 - 2*q$. the same method can be used to show that the weil polynomials with $a = 0$ and with other values of b (subject to certain elementary restrictions) *do* occur; this was carried out by daniel maisner. these results, combined with earlier work, allow us to easily determine the weil polynomials that arise from genus-2 curves with ordinary jacobians.