An algebra problem by Sourabh Jangid

Algebra Level 4

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): \(bd + ae \ne 0 \).

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