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we have to solve for y(n)

\[y(e^{jw})(1-5e^{-jw}+6e^{-2jw})=0\]
let s=e^jw
\[y(s)(1-5/s +6/s^2)=0\]

\[(1-5/s +6/s^2)=0\]
\[(1-3/s)(1-2/s)=0\]

\[(1-3s^{-1})(1-2s^{-1})=0\]

s=-3,-2

I think the roots are +3 and +2
(I would have solved s^2 -5s +6=0 to get (s-2)(s-3)=0

yes, s=3 and s=2

then how would we go back to fourier form?

this reminds me of laplace transforms, but I have not seen it done using fourier

z transform since it is discreet

I would have to read up on it, because I don't know this off the top of my head.

ok, thanks

btw, what kind of problem is this?

this is from discrete signal processing