2.48 For the equations $x^{2}+c x+2=0$ and $x^{2}+2 x+c=2$, which of the following conclusions is correct?
(A) At least one equation has real roots.
(B) At most one equation has real roots.
(C) Both have real roots.
(D) Neither has real roots.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991)
[Sol] Let the discriminants of the two equations be $\Delta_{1}$ and $\Delta_{2}$, respectively, then $\Delta_{1}=c^{2}-8$, and $\Delta_{2}=4-4(c-2)=12-4 c$. And $\Delta_{1}+\Delta_{2}=c^{2}-4 c+4=(c-2)^{2} \geqslant 0$, so at least one of $\Delta_{1}, \Delta_{2}$ is non-negative, thus at least one of the equations has real roots. Therefore, the answer is (A).