So basically if I have a polynomial with roots r, s, and t, how do I find the polynomial with roots 1/r, 1/s, and 1/t, or how do I find the polynomial with roots 2r, 2s, or 2t? Could you please give me a generalization too? Thank you so much
By vieta's formulas, given a cube(it can be any polynomial) ax3+bx2+cx+d = 0
and roots r,s, and t:
r+s+t = -b/a
rs +rt + st = c/a
rst = d/a
you could try solving for these values in terms of the ones that you want(for example, with 2r, 2s and 2t, rewriting these equations using those respective terms). I'm sure that this would be one approach that would work.
If you want more information to learn more about vieta's, the internet is always a great tool to search up information regarding it.