Means, Monics and More

The arithmetic mean, the geometric mean and the harmonic mean of the roots of the polynomial $\begin{aligned} P(x) = x^{100} - 2 x^{99} + 3 x^{98} - 4 x^{97} + (\cdots) - 100x + 101 \end{aligned}$ are the only roots of the monic polynomial $Q(x)$ .

Evaluate the sum of all true statements.

(0) = There are no true statements.

(1) = $AM > GM > HM$ .

(2) = $P(x) > Q(x), \: x \in \mathbb{R}$ .

(4) = $Q(0) > 2$ .

(8) = $P(x)$ has no real roots.

(16) = $Q(Q(x))$ has 6 real roots.