For the Extension 2 seminar, I will compile a short list of 20 or so "Question 8" type questions which include things that HAVE been tested in the past, but not actually taught as a topic. This includes:
- Location of polynomial roots "Prove that all the roots of P(x) lie in the circle |z| < r"
- Prove that if we have XXXX condition, then the relationship between the coefficients is YYYY. Now, I'm not talking about the pansy ones like "Prove that if the roots are in A.P, then etc etc" which you will find stock standard in a textbook. I'm taking about harder ones like "What is the condition on a_1, a_2 , a_3, ... , a_n if the roots of the polynomial P(x) are the the vertices of (some polygon)" which form a link between the geometry of the roots and the coefficients of the Polynomial.
- Prove that P(x) has a rational root lying in the interval x E [a,b]
- Some properties of Reciprocal Polynomials, including the real reason why they are called Reciprocal Polynomials!
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On a lighter note, just found out my cousin is in the Kookies & Kream dance team in the "Australia's Got Talent" semis! I loved the Skrillex Dubstep part =)
"Yes! Oh my god!"
*bass*
They performed at our school a few weeks ago, it was great!
