Suppose that PQR is a 50-60-70 (respectively) triangle with an interior point X. Let angle PXR = s and angle QXR = t.
Find (in terms of s and t) the three angles of any triangle with side lengths equal to PX, QX and RX.
Exactly one real root and no complex roots when k=+/-1.
For other real values of k, there are 3 roots according to the Fundamental Theorem of Algebra, one must be real according to the Conjugate Roots Theorem.
Re: HSC 2014 4U Marathon - Advanced Level
Sorry That I am doing it again.
If x^2 + y^2 = 1 in your last example?
Have you got a counterexample for zero degree cyclic rational functions?
Thanks for your patience.
To make clear, I wasn't trying to make any claim at the start, purely to do Sy's...