Here is a fun problem. It was in the Pre-Calculus book that the local highschool uses, so my dad teaches from the book and I tutor from it. It was in a calculator-use section that asked for an estimation of roots only, not an algebraic solution, but just for fun, why not solve it algebraically? :-D I admit that Father Dear discovered the key to solving it, though I carried it through and found the ghastly solutions :-P.
Find all roots of the equation x^3 - 3*x^2 + 3*x + 2 = 0.
You must use high school mathematics concepts only. In other words, don't use the cubic formula!!!