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I assume 2 posts was a mistake.
Quick format, just re-wrights the index, so no it would not find bad sectors.
Seems to me the last time I played with a hard drive with bad sectors, I had to go back to a win98 format, to mark bad sectors, as I don't think XP or newer dose that.
I think it just tries to repair.
The hard drive manufacturer, has a downloadable disk, that will test the drive. Unless it is one of the crappy brands.
This is a very accurate test, and can be trusted.
I don't thing anybody tries to recover a failing disk anymore, but another option that works, is watch at what percentage the format stops.
Say it is 75%.
Then partition the drive to 70%, and leave the rest unpartitioned. I had a drive last for years after doing that.
Of course, if format fails @10%you would loose 90% of the drive.
Really nothing I would do today.