2 If $\alpha, \beta$ are two distinct real roots of the equation $x^{2}+p x+8=0$, and $|\alpha|>|\beta|$, then among the following four conclusions, the one that does not necessarily hold is ( ).
(A) $|\alpha|>2$ and $|\beta|>2$
(B) $|\alpha|+|\beta|>4 \sqrt{2}$
(C) $|\alpha|>\frac{5}{2}$ or $|\beta|>\frac{5}{2}$
(D) $|\alpha|>2 \sqrt{2}$ and $|\beta|<2 \sqrt{2}$