Quad core processors need more power to work.
The reason why you get BSOD(s) is because when you attempt to do something more than NOTHING such as installing/uninstalling something,executing something and so on...,processor needs to process more informations and perform a LOT of calculations very fast and in order for the processor to do that (especially with ALL 4 cores),it logically needs more power in order to be able to do that.
You can always increase the voltage and see if that helps.Just be careful to not increase it too much otherwise you can burn the processor and EVEN the motherboard if you adjust all the voltage types incorrectly lol.
On some laptop motherboards even with the right voltage,quad core processor do not work very well.They are just not designed to work well with quad core processors EVEN if you do have quad core processor which fits in your socket on the motherboard.
Most of the laptops are designed for dual cores and DO work well with them.Not all laptops work properly with quad core processors.
Believe me you do NOT need quad core processor ESPECIALLY if it's for your homework lol.Unless if you are programming crazy staff like I do which needs to execute tons of programming lines of code and perform tons of calculations every milisecond lol
But I am pretty sure you do not do that,so BELIEVE ME dual core processor is MORE THAN ENOUGH for you
As for the RAM memory...you do NOT need probably even more than 2 GB.
I mean do you really use 6 GB of RAM memory ALL THE TIME lol??? I don't think you do lol.So if lt's say you have 4 GB of RAM and you add 2 more,computer will NOT work any faster unless if you REALLY REALLY REALLY use 6 GB of RAM memory ALL THE TIME,but I am pretty sure you don't especially if it's for a simple homework lol.
As for the RAM slots.If let's say you have 4 RAM slots and have 4 GB of RAM memory:
It is better to have 1 GB of RAM memory in EACH slot rather then have 4 GB of RAM memory in one single slot.
But even if you have it all in one slot,you will NOT see any difference at all unless if you do crazy programming staff which requires that lol.But like I said...I am pretty sure you don't do that.
O and by the way...if you think that your strong dual core processor is weak and that you need MORE RAM memory then you should try mine: AMD Athlon XP 1700+ and RAM is just 512 MB DDR1.
Now THAT is weak man.It has ONE SINGLE WEAK core of just 1.4 ghz and it's not even close to your dual core processor.And still I manage to find a way to run 25 programs at once and have up to 63 processes running all the time without any problems at ALL.Plus I did not reinstall my operating system since 2004 and still works perfectly.People spend so much money on buying new hardware every year or every 2 years and sometimes even more often.While on the other hand I do that only ONCE in 15 years and still manage to do all the work completely the same just like other people.With one small difference.They spend so much money on the STRONGEST quad core processors and other expensive hardware components while I do not spend a single dollar lol.
The only reason why somebody would need so strong hardware is if he/she is a crazy game player who plays 3 games at once all on the BEST graphic quality and ONLY then

Otherwise who the hell needs so strong hardware for so simple things lol...
Don't spend so much money on something you do not need believe me
So if you need so strong processor and SO MUCH RAM memory for so simple things like homework and still it works slow then you are using your computer incorrectly lol.

Your operating system is either in a CRAPY condition or you simply use your computer incorrectly lol.
Cheers!