2・108 $2 \cdot 108 p^{2} \geqslant 4 q$ is the condition for the real-coefficient equation $x^{4}+p x^{2}+q=0$ to have real roots
(A) A necessary condition but not a sufficient condition.
(B) A sufficient condition but not a necessary condition.
(C) A necessary and sufficient condition.
(D) Neither a sufficient condition nor a necessary condition.
(China Northeast Three Provinces Mathematics Invitational Competition, 1989)
[Solution] If we let $x^{2}=t$, the given equation can be transformed into $t^{2}+p t+q=0$, which has real roots if and only if $\Delta=p^{2}-4 q \geqslant 0$, i.e., $p^{2} \geqslant 4 q$.
However, the real roots of this quadratic equation do not necessarily guarantee that the original equation has real roots.
Conversely, if $p^{2} \geqslant 4 q$ does not hold, then the original equation definitely has no real roots.
This means: $p^{2} \geqslant 4 q$ is a necessary condition for the given equation to have real roots, but it is not sufficient. Therefore, the answer is $(A)$.