Monday, March 9, 2015
[IB-HL H&H_Rev6C Q11] Factors of a Complex Polynomial
IntroductionThis question is taken from the Haese & Harris textbook for IB HL Mathematics and is rather challenging. Here I present two solutions. In the first solution, I use substitution to make a variable “disappear”. [ heuristics: H10. Simplify the problem, H11. Solve part of the problem] And that allowed me to crack the rest of them problem. In the second solution, I rephrased the problem in terms of tangents to curves. [ heuristic H09. Restate the problem in another way ] This gives another angle from which to tackle the problem.
Both solutions are related in the sense that they hinge on some form of the relation maked as [*]. That led to an equation in a. Once a is found, k can be found, and the solutions proceed similarly. The equation [*] is a manifestation of the fact that for a repeated root, both P(x) and P’(x) share a common factor.