I have access to root and would like to find out.
That should give info about how many cores are available and which type they are.
The place to look is /proc/cpuinfo, as others have said. However, at a glance this does not tell you whether a server is dual-core. If you see two entries, it could be because
For example, take this information from cpuinfo.
I can see that there are 8 logical processors, but I don't know how many CPUs and cores there are.
Now I know there is only one CPU, but I don't know if it has 8 cores or 4 cores and hyperthreading.
Now I have the complete picture; this is a single quad-core CPU with hyperthreading.