Irreducible polynomial clarification

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I am not sure if the polynomial: $f(x) = x^3 +1 \in \mathbb Z / 3\mathbb Z$ has roots. I think that it has a root $x = 2$ because $2^3 + 1 \equiv 0(\mod3)$ Is this true? because my professor claimed today that is has no roots, maybe he was confused with something else or I am the one who is wrong...