In this article we give necessary and sufficient conditions for an irreducible K¨ahler C-space with b2 = 1 to have nonnegative
or positive quadratic bisectional curvature, assuming the space is not Hermitian symmetric. In the cases of the five exceptional Lie
groups E6,E7,E8, F4,G2, the computer package MAPLE is used to assist our calculations. The results are related to two conjectures
of Li-Wu-Zheng.