You can suppose A=1.
So write for the auxiliary equation. Since it has real coefficients and a complex root, its conjugate is also a root.
Suppose we are given two roots, and , of a cubic auxiliary equation which has real coefficients. Determine what the corresponding homogeneous linear Dif EQ is.
So wouldn't we have Am^3 + Bm^2 + Cm + D = 0, and when we solve that for m we get the two values listed above. Not sure how to do this..