  In this article we give necessary and sufficient conditions for an
irreducible K\"ahler C-space with $b_2=1$ to have nonnegative or positive
quadratic bisectional curvature, assuming the space is not Hermitian symmetric.
In the cases of the five exceptional Lie groups $E_6, E_7, E_8, F_4, G_2$, the
computer package MAPLE is used to assist our calculations. The results are
related to two conjectures of Li-Wu-Zheng.
