A problem my high school math teacher would have loved

Earlier tonight a friend of mine sent me a link to some old problems from a middle school math contest in California.

Berkeley Math Tournament middle school problems

I skimmed through the 2014 contest for fun and ran across a problem that my high school math teacher – Mr. Waterman – would have loved:

#16: Consider the graph of A line intersects this cubic at three points, two of which have x-coordinates 20 and 14. Find the x-coordinate of the third intersection point.

I’m a little surprised (to say the least!) to see a problem like this on a middle school test, but it is a really cool problem. Properties of roots of equations was one of Mr. Waterman’s favorite subjects.