For a positive semi-definite biquadratic forms F in (3, 3) variables, we prove that if F has a finite number but at least 7 real zeros Z(F ), then it is not a sum of squares. We show also that if F has at least 11 zeros, then it has infinitely many real zeros and it is a sum of squares. It can be seen as the counterpart for biquadratic forms as the results of Choi, Lam and Reznick for positive ...