About a year ago I asked on MO when a Newton basin fractal is continuously determined by the roots of its polynomial. I mentioned in that question that I had convinced myself that the roots of the polynomial must all be simple, and nobody in the answers or comments called that out as wrong *or* as obvious.

I'd like to nail down whether this result is correct, already known, interesting etc. Is it appropriate for me to post a question (suitably elaborated) like:

Is this "fact" I mentioned in my other question already known? Is it even correct?

It's basically a reference request, but it's also pretty close to a "here's my work, please give me feedback" kind of question, which makes me hesitant to post it on MO without checking meta first.

notask anyone to read my work. Thanks! $\endgroup$