to play multiplayer you will need a quad core to play smoothly also your gfx wont give you high or ultra. it will give a mix of high and medium. dont forget to turn blur off or you will incur a heavy hit on the gpu.
the 7750 isnt a strong gfx card. its low midrange but should work well enough on your small screen. as far as gaming goes. it will max out a lot of older titles like call of duty 4,5,6 @720p but bf3 punishes even the best cards due to poor clipping on some maps.
but like i said your cpu will likely cause the biggest issue as the frostbite engine needs a quad to run smoothly or it wont let you max out the performance of even the most poultry of cards. a gtx 270 for instance ( a good card 3 years ago) will bounce between 40 and 5 fps when paired with a dual core on bf3 but will give 125 fps solid on cod 4.
if you can live with fps bounce then feel free to ignore everything i posted... im just trying to save you some money on a game i know doesnt work very well on a dual core setup.
on some maps the game is smooth to play but on others it will crumple your system. so i wont stop you but i did warn you.
http://www.youtube.com/watch?v=Ow50hAcVQcg this is the comparison of a 7750 on both low and ultra settings and this is on an empty server. never take what you see on the web as truth until you can verify it...
yes he's playing at 1080p but that wont make much difference on a card that has more than 768mb of ddr5 maybe 4-5 fps in light load areas.