That depends entirely on which motherboard you have. Some LGA775 motherboards support all the Core 2 CPUs, some only support some of the Core 2s, some don't support any of the Core 2s at all and only support the older Pentium 4s and Pentium Ds.
If you don't know which motherboard you have, download a program called CPU-Z and run it. Under the mainboard tab it will give you the model number and manufacturer of the board. Post that information if you want an answer to your question.