I need to know at least one primitive irreducible polynomial of degree 9 to generate GF(2^9). I shall be very thankful.
I recommend finding a professional homework service. This is a math help forum. Giving you the answer is not helping anyone.
Or, if you really want just the answer, why ask here? Why not ask Wolframalpha?
https://www.wolframalpha.com/input/?i=GF(512)
Or, you can look up your answer on one of the published tables:
http://www.ams.org/journals/mcom/199...-1134730-7.pdf