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Hi all, I have a question for which I have included a poll for you to vote on below: Suppose that a textbook is to be written for the extension 2 new syllabus that is set to include very detailed solutions, such that the book would most likely become too big and heavy if everything was all...

Just a fun question I made up.

\large \text{Let } P(z) = 2z^{4} + 5z^{3} + 7z^{2} + 5z + 2. \\ \text{ Without solving } P(z) = 0, \text{ prove that } P \text{ has no real roots.}

Hi all, Attached are my set of fully worked solutions for the 2004 HSC MX2 exam. They are complete with detailed explanations, multiple methods to selected questions, and remarks proceeding an answer or result to highlight certain subtleties that students would perhaps miss, or simply to...