Students will be well acquainted with the solution of the quadratic equation and may have found out about al-Khwarizmi and his work. It took about 800 years from the solution of the quadratic to that of the (general) cubic. Khayyam's work dates from that end of the first half of that period. There are plently of calculations to do here, and algebra too! Students will find it interesting to see the interaction of algebra and geometry, and how the story unfolded over the centuries.
To motivate the need for such solutions, students will realise that [math]x^3+9x=26 [/math] is easy to solve by factorization, but what about [math]x^3+9x=25[/math]? The problem also provides a good setting for discussion of the development of notation and of numbers, negative and complex numbers, in particular.
