Finding Roots of Irreducible Polynomials in Z5

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F= x^3 + 2x + 1 irreducable in Z5 (Z subscript 5)

i have tried EC looking at F(x+1) which doesn't work for me. Cant think of what else to try.

Help much appreciated. Need to know this for an exam later! ahhh
 
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irreducibility of a cubic over a small finite field is trivial because it suffices to show there are no roots.
 
Ok so the only possible roots are 1 2 3 4 or 5 is this correct? Thanks so much for your reply! i have an exam is a few hours with this on it!

Edit: or is +-1 the only possible roots? Thanks again
 

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