An algebra problem by Sourabh Jangid

If the non-constant function $f(x) = \dfrac{ax^2 - bx+ c}{dx^2 + ex - c }$ is a bounded for non-zero constants $a,b,c,d$ , then which of the following are true?

(A): $d$ and $c$ have the same signs.
(B): $d$ and $c$ have opposite signs.
(C): $bd + ae = 0$ .
(D): $bd + ae \ne 0$ .