Coefficients of a transfer function

[magnifik]

for a system defined as y(n) + a₁y(n-1) + a₂y(n-2) = bx(n), for what values of a₁, a₂, and b is the system realizable?

i know that the transfer function is obtained by the following
H(z) = Y(z)/X(z)
H(z) = b/(1 + a₁z^-1 + a₂z^-2)
H(z) = bz²/(z² + a₁z + a₂)

i also know that the poles have to be in the unit circle to be BIBO stable and that the ROC should be right sided for it to be causal as well. but I'm unsure on how to determine the conditions on the coefficients.

 

[MisterX]

You can use the quadratic formula to express the poles of the transfer function in terms of the coefficients a1 and a2.