4. Let proposition $P$ : 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 $P$
(D)
4. 【Analysis and Solution】For example, the solution sets of $x^{2}-3 x+2>0$ and $-x^{2}+3 x-2>0$ are different, thus eliminating $(\mathrm{A})$ and $(\mathrm{B})$; also, the solution sets of $x^{2}+x+1>0$ and $x^{2}+x+3>0$ are the same, thus eliminating (C).