Question 108
Find all pairs $(r, s)$ of real numbers such that the zeros of the polynomials
$$
f(x) = x^{2} - 2 r x + r
$$
and
$$
g(x) = 27 x^{3} - 27 r x^{2} + s x - r^{6}
$$
are all real and nonnegative.
$$
f(x) = x^{2} - 2 r x + r
$$
and
$$
g(x) = 27 x^{3} - 27 r x^{2} + s x - r^{6}
$$
are all real and nonnegative.