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F.<alpha> = GF(9)
R.<x> = PolynomialRing(F)
f=x^3+2*x+1
f.roots()
[] 

F.<alpha> = GF(3^6)
R.<x> = PolynomialRing(F)
f = x^3+2*x+1
f.roots()
[(2*alpha^5 + 2*alpha^4, 1), (2*alpha^5 + 2*alpha^4 + 2, 1), (2*alpha^5 + 2*alpha^4 + 1, 1)]