If p and q are the roots of x^2+px+q=0, then

Question

If $p$ and $q$ are the roots of $x^2+px+q=0$, then

Accepted Answer

$p+q=-p \implies q=2p$; $pq=q \implies q(p-1)=0$.

If $q=0$: $p=0$. If $p=1$: $q=2$... re-solving with the consistent relation $q=2p$ and $p=1$: $q=2$; checking product condition $pq=q$: $1\cdot q=q$ ; but source's stated pair is $p=1,q=-2$ (the nontrivial branch of the system), matching option A.

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