I love problems like this! Very cool...

@comment: Hehehee! Thank you very much!

So then "Bite Me".

Yeah, I wasn't sure whether you had it or not. Great work!

Your first intuition gives the first valid solution that has been posted. This is success worth building on...

Is this the edit you mean?

"Assuming that a and c are positive, we get p(x) = (x-c)(x-d) and q(x) = (x-a)(x-b). p(x) = x^2 - cx - dx + cd and q(x) = x^2 - ax - bx + ab. This gives us
a = -c-b
b = cd
c = -a-b
d = ab
Substituting gives us a = d/b and b/d which implies that d=b which means that principle iii is in violation.

Assuming that a and c are negative, we get p(x) = (x+c)(x+d) and q(x) = (x+a)(x+b). p(x) = x^2 + cx + dx + cd and q(x) = x^2 + ax + bx + ab. This, in turn, gives us
a = c+d
b = cd
c = a+b
d = ab

Which allows us to posit that a = a + b + d (via substitution for c) which means that b = -d. And with a little plugging in a = c = -1. Thus:

p(x) = x^2 -x + 2
and
q(x) = x^2 -x - 2

are in S."

The problem with this is that p(-2)=8, not zero; and p(-1)=4, not zero.

Also, when you get the solution, you find that a is NOT d/b.

You are very close... closer than anyone else. You need to go back to your "first intuition".

I love your avater! Not many people can tell a story in a 115x145 jpeg!

Wanna come over? LOL!!!

Merry Christmas!

Happy Thanksgiving!

Meh @ Marble Hornets.

The top Google result for that line is this: http://www.lems.brown.edu/~pas/misc/...ublic-dogs.txt

haha, your avatar and signature made me laugh

I have nothing against him, so I wouldn't offend him on purpose.

LOL, no! I made a joke - that he feels like drinking the toilet water instead of vomiting (what he had suggested), because that's what that pic actually shows, anyway.

I really do. Considering the average age of the people on INTJf, there are probably many of us with PCOS on here, they just don't know it yet.

Sorry, I think it's an NF thing =D You have many skills that I lack, no doubt.

hee, you never saw that happen?

ah thanks...well was discussing it and though your theory is right at times, the application is a bit off...