Let the roots of the equation $x^2+px+q=0$ be $p$ and $q$.

Using Vieta’s formulas for the quadratic $x^2+px+q=0$:

• Sum of roots $= -p$
• Product of roots $= q$

Since the roots are themselves $p$ and $q$, we get: $p+q=-p$ and $pq=q$

Solve these equations.

From $p+q=-p$ we get $2p+q=0$ $q=-2p$

From $pq=q$ we get $q(p-1)=0$

So either:

Case 1: $q=0$

Then from $q=-2p$, $0=-2p \Rightarrow p=0$ So one solution is $(p,q)=(0,0)$ which is not among the options.

Case 2: $p=1$

Then from $q=-2p$, $q=-2(1)=-2$ So another solution is $(p,q)=(1,-2)$

Check the options:

• A: $(p,q)=(1,-2)$ ✓
• B: $(0,1)$ ✗
• C: $(-2,0)$ ✗
• D: $(-2,1)$ ✗

Hence the correct option is: $\boxed{A}$