I need to find the minimum $r$ and the maximum $k$ of the following cubic equation for which there does not exist three distinct real roots.
$rx^3-rkx^2+(r+k)x-rk=0$.
Is it possible to find such $r$ and $k$ analytically? Or if you can provide me help using mathematica, that would be fine too.Thanks.
Reduce[Discriminant[r x^3 - r k x^2 + (r + k) x - r k, x] == 0, {r, k}, Reals] // FullSimplify
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