4.3 Let proposition $P$ be: the solution sets of the inequalities $a_{1} x^{2}+b_{1} x+c_{1}>0$ and $a_{2} x^{2}+b_{2} x+c_{2}>0$ with respect to $x$ are the same; proposition $Q: \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$. Then proposition $Q$
(A) is a sufficient and necessary condition for proposition $P$.
(B) is a sufficient condition for proposition $P$ but not a necessary condition.
(C) is a necessary condition for proposition $P$ but not a sufficient condition.
(D) is neither a sufficient condition nor a necessary condition for proposition $P$.
(China High School Mathematics League, 1998)
[Solution] Notice that the solution sets of $x^{2}-3 x+2>0$ and $-x^{2}+3 x-2>0$ are different, thus eliminating $(\mathrm{A}),(\mathrm{B})$;
also, $x^{2}+x+1>0$ and $x^{2}+x+3>0$ have the same solution set, thus eliminating (C). Therefore, the answer is (D).