Feathers on my duck's back and tail look bad
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Does she have access to water to bathe in?
How long has this issue been going on?
Since you just got her, it is likely from something going on where she was.
Was she outnumbered by drakes? Did she have water to swim in? What was the food she was getting?
At this point, I would suggest getting poultry vitamins - put those in her water (according to instructions - some powders you just put a quarter teaspoon per gallon of drinking water) once a week. And I would give her fresh water to swim and splash in every day, all day if she wants. I would get her on a good quality complete food. There are several of them. I'd make sure she gets some rest - are there drakes in your flock? She may need a break from them.
Once feathers are damaged, it takes a while for them to be replaced. Adding just a little extra protein to the feed (I use dry good quality cat kibble) can help.
Please keep us posted.