Question

p2+2pq+q=1 ?

Answer 1

is that q^2 also?

Answer 2

(p+q)^2 =1
sqrt both sides
p+q =1
so an infinite number of solutions

is the question p^2+2pq+q^2=0

Answer 3

I suppose it could also be a quadratic in p (with a not "nice" answer).