解:當(dāng)???$x=-1$???時(shí),???$x^2+px+q $???的值是???$-5;$???當(dāng)???$x=3$???時(shí),???$x^2+px+q $???的值是???$3,$???
?$ 把它們分別代入方程,得$?
???$ {{\begin{cases} { {1-p+q=-5①}} \\{9+3p+q=3②}\end{cases}}}$???
由①得,???$q=p-6③$???
?$ 把③代入②,得$?
???$ 9+3p+p-6=3$???
解得,???$p=0$???
把???$p=0$???代入③,得
???$ q=-6$???
所以???${{\begin{cases} { {p=0}} \\{q=-6}\end{cases}}}$???