Need Assistance with proof of the existence of conjugate complex roots

Prove:

given that f(x) = Anx^n + An-1X^n-1+ ....A1X + A0 , and An does not = 0

=> if f(x) has a root of the form (A+Bi),then it must have a root of the form

(A-Bi). (complex roots)

All I can figure out so far is to utilize the Conjugate Roots theorem but our professor gave us a hint that we should use the Remainder theorem? or the discriminate? I'm not quite sure but basically I need to Prove why the conjugate exists in the polynomial.

Regards, Chris