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does the dell inspiron 531 support a quard core processor?

Sadly, no, the highest you can go is the AMD Athlon 64 X2 6000+, which is a 3 GHz dual-core. Even then, you might encounter problems with power consumption and/or heat output (or flat out failure to boot) that give uninformed users fits on some OEM boxes. Running CPU-Z on your PC and linking a screenshot of the CPU tab is the easiest way to get help on a compatible upgrade.