This problem gave my son some trouble this morning:
Problem #19 from the 2011 AMC 10b
The problem asks you to find the product of the roots of the equation:
A lot of ideas from Algebra come into play on this problem and we had a good conversation about it tonight.
We started by talking through his ideas about the problem and found a couple of interesting misconceptions about algebra and equality right at the beginning:
Next we went back to look if the 4 solutions that we found to the equation were actually solutions:
Finally, I went back through the problem to show him how the 3 and -3 showed up even though they are not solutions.
The emergence of these spurious solutions makes this a really instructive problem.
Mike's Math Page 