My answer would be q = -x^2 – xp, pick any value of p you want.This is a nice problem.It is not hard to solve. ]]>

p^2 + p^2 + q = 0

q is a solution iff

q^2 + pq + q = 0

taking q = 0 we get p = 0

if q is not 0 then 2nd eqn becomes q + p + 1 = 0

using this and 1 we get

2p^2 – p – 1 = 0

which has 2 solutions p = 1, p = -1/2

and corresponding q’s

So this approach somehow misses p = -1/2, q = -1/2

hehe the author of this question definitely had his own style of sense of humour. ]]>

Find numbers p and q such that x=p and x=q satisfy x^2+px+q = 0.

]]>If p is a solution of x^2+px+p=0, then we have p^2+p^2+p=0. From that, p could be 0 or -1/2. We already got the solution p=q=0, but p=q=-1/2 is a new possibility.

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