Hey can i run battlefield bad company 3 my pc spec intel dual core processor e21

yes it will run but bad company really needs a fast quad core. dualcores tend to bottleneck as the game is badly coded for them. your settings are likely to be medium low but turn off dx11 as this will give a sizable fps boost(comparatively)... yes your card may support dx11 but it doesn't have the grunt to run it, so disable it. you will also need to oc the cpu to 2.5ghz at the very least.(so you may want better cooling as you dont oc on stock cooling EVER!.