Complex roots of polynomials with real coefficients occur in conjugate pairs, so the number of complex roots is even (here complex means non-real).

A polynomial of odd order has at least one real root.

That should allow you to decide on A, B and C. A suitable choice of signs for a, b, c, d, e and Descartes rule of signs will allow you to decide on E.

Which leaves D (which is false can you see why?).

CB