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High Quality Content by WIKIPEDIA articles! In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree. In other words, if P is a non-constant homogeneous polynomial in variables X1, ..., XN, and of degree d satisfying d N then it has a non-trivial zero over F; that is, for some xi in F, not all 0, we have P(x1, ..., xN) = 0.