Re: [math-fun] solving, denesting, and reading comprehension

Bill Gosper <billgosper@gmail.com> writes:

Wow, 78 roots, two real. Here's one of those: [...]

A trinomial can never have more than two real roots (Descartes' rule). For the 72-element group, a general formula is 27*x^6 + 9*t^3*(t+8)*x + t^3*(t+8)*(t^2+7*t+1) = 3*A^2 + t*(t+8)*B^2 where A = 3*x^3 - t*(t+8)*x/2 - t^2*(t+8)/2 B = (6*x^2 + 3*t*x - (t^2+2*t)) / 2 it seems that this has a real pair of roots *iff* -8 < t < 0. NDE