I'll give it a try
let's first cancel out x^2
y(y+2x)<0 -> Great! St 2 is TRUE and possible, isn't it?
what follows afterwards is not very reliable
Case I: y<0 and y+2x>0 -> y>-2x -> -y
[this is positive]<
[the sign flips]2x
[if 2x is greater than a positive number, than x is positive]
Great! St 1 is possible because y is negative and x is positive , but this also means that St 3 is possible because a negative number is always smaller than a positive one.
Don't think it is necessary to go ahead with Case II, since the question asks only for possibility, not necessity
Hope this helps and the other guys correct me as long as I'm wrong
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