Mathematics

The key is to use the ratio between the roots to express them in terms of a single variable, then apply Vieta's formulas. If the roots are in ratio $1:3$, call them $r$ and $3r$ where $r > 0$. Their product gives you $r$ directly, and their sum gives you $p$—but remember that $p$ is the negative of the sum of roots for a monic quadratic.

The key is to use the ratio between the roots to express them in terms of a single variable, then apply Vieta's formulas. If the roots are in ratio $1:3$, call them $r$ and $3r$ where $r > 0$. Their product gives you $r$ directly, and their sum gives you $p$—but remember that $p$ is the negative of the sum of roots for a monic quadratic.