Whether a negative number is an extraneous root or not can be context dependent. Y'all have probably heard those word problems like the three guys and a monkey on a desert island. They gather a pile of coconuts and agree to divide them up equally among themselves. The effort of gathering the coconuts has worn them out so they agree to divide them up in the morning, but guy 1 gets up in the middle of the night and counts out the coconuts into three piles with one left over. He takes his third and stashes them and gives the one left over to the monkey. The second guy does the same thing a little later, dividing the pile into three (with one left over), taking his third and giving the one left over to the monkey. The third guy does the same thing and in the morning they find the pile still has one left over after dividing into three. The question is how many coconuts there were to start with and somebody found a solution with a negative number of coconuts.
Note: This problem is dredged out of my JDM and may not, in fact, have any solution so doen't try to solve it. It is only here as an example.
