Chromebook 11 3120 battery draining when supposedly off - and beeps when in "developer mode"

Earlier this year I bought a Chromebook 11 3120 and I have been greatly disappointed with its battery life as even when shutdown it drains the battery!

Is this normal behavior for a Chromebook?

I don't think so...

Even though it takes >10 hours to drain the battery from full charge it is rather annoying having to plug the thing in each day when with the little use it gets it should last a week or more without needing a recharge.

Also, if I enable developer mode, the thing emits a random "beep! beep!" when supposedly shutdown/switched off, which leads me to believe it is faulty and not actually powering down and staying down.  The beeps are the same as when booted in developer mode and left 30 seconds as it is the warning that OS verification is disabled.  

When the normal ChromeOS is restored (by either doing a full recovery or simply pressing the space bar at the warning screen when booting), the beeping does not occur, but the battery still drains when the thing has been shutdown.

Does anyone else with a Dell Chromebook experience similar issues?