Cubic function : Roots[f] Search
A student and I were trying to find roots of f(x) = x³ + (k - 6) x² + (2k - 1) x + 30 by varying k on a slider, and using Roots(f).
One of the expected roots is x = -2 since (x+2) is always a factor of f(x) regardless of values of k.
But remaining 2 roots of cubic function depend on values of k.
We were trying to find the repeated root. We set system to 12 decimal places trying to get as close to the repeated root as possible, by varying k and observing the graph
Near to the repeated root we unexpectedly found 4 roots instead of 3. Can we check if there's some algorithm weakness in the system in using Roots to find the roots?