1. If one root of the equation $x^{2}+p x+q=0$ is twice the other, then the relationship satisfied by $p$ and $q$ is $\qquad$ .
1. $2 p^{2}=9 q$

Solution: Let the two roots of $x^{2}+p x+q=0$ be $\alpha, 2 \alpha$, then $3 \alpha=-p$, and $2 \alpha^{2}=q$.
Eliminating $\alpha$, we get $2 p^{2}=9 q$.