(Spoilers!) Comments and discussion on Valentin's 5th "Then and Now" - Roots

[EdS2]

This thread is an offering to anyone and everyone who would like a place to discuss or digress on Valentin's latest challenge thread:
[VA] SRC #012e - Then and Now: Roots

Beware: there will probably be spoilers within. You are encouraged to read the challenge carefully, have a good think, and try to solve it before exposing yourself to the thoughts of others.

As Valentin does set some splendid challenges but strongly prefers a clean thread for later publication, here's a place where we can discuss our approaches, show any mathematical analysis, use any tools, calculators or computers which might help us to enjoy the challenge.

My aim is only to collect those posts which are not within Valentin's rules - please continue to post in the original thread, especially with your solutions as requested over there.

I do this in a spirit of friendly collaboration, hoping that one strict thread and one loose thread will be a good combination which can keep everyone happy. As such, please no argumentation about the way Valentin runs his challenges - let's stick to the calculations, the mathematics, the analysis.

Links to tangentially related papers, discussions, videos, are all very welcome.