Viète's Results: Cubic & General Polynomials

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Whoaaa thank you so much, sir, for clarification on how the pattern really is! :D
This video really is what I needed: I was confused on how there seems to only be a general sum formula and a general product formula but then for some reason there are sums of products for higher order polynomials, and how this generalizes, as well as how the formulas will turn out.
But this video cleared it all out for me, with the "sum of the roots, n at a time" pattern. Thank you so much!
EDIT: I think this video is underappreciated.

bismajoyosumarto
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the changing signs are a part of the pattern, right?

ryyn
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