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First thing, uninstall the 3rd party app/task killer... They have been proven regardless of what you read by the developers to be your worst enemy. We have plenty of articles and blogs about task killers doing strange things to your device written here at AC.
Otherwise simply rooting your device will not change things. If your still on a stock ROM and kernel nothing should have changed other than obtaining Superuser Access (root) and custom recovery being installed (ClockWorkMod).
I would try looking over the various kernels and look for the ones with the best reports for good battery life and try flashing one of those. Preferably something that has a undervolt for your CPU like instead of the stock 100 Mhz-1000 Mhz clock speed your CPU runs at, try one that allows your to bump it down to 100 Mhz- 800 Mhz. Then you also have the choice of governers (different profiles at which your style of use fits you and it adjusts the device/kernel).
Hope this helps...