AHSME 1993 Problem 20

Consider the equation $10z^2-3iz-k=0$, where $z$ is a complex variable and $i^2=-1$. Which of the following statements is true? $\text{(A) For all positive real numbers k, both roots are pure imaginary} \\ \text{(B) For all negative real numbers k, both roots are pure imaginary} \\ \text{(C) For all pure imaginary numbers k, both roots are real and rational} \\ \text{(D) For all pure imaginary numbers k, both roots are real and irrational} \\ \text{(E) For all complex numbers k, neither root is real}$