$65 p^{2} \geqslant 4 q$ is the condition for the real-coefficient equation $x^{4}+p x^{2}+q=0$ to have real roots
A. A necessary but not sufficient condition
B. A sufficient but not necessary condition
C. A necessary and sufficient condition
D. Neither a sufficient nor a necessary condition
65 A. Let $y=x^{2}$, then the original equation can be transformed into
$$
y^{2}+p y+q=0 \text {. }
$$

The original equation has real roots if and only if the above equation in $y$ has non-negative real roots. It is easy to see that $p^{2} \geqslant 4 q$ is a necessary but not sufficient condition for the above equation in $y$ to have non-negative real roots, hence the answer is A.