Solving Equations & the Conjugate Root Theorem

Solving equations and the conjugate root theorem is part of the Complex numbers topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-03). This subtopic solves quadratic equations \(ax^2 + bx + c = 0\) with complex coefficients, and recognises that quadratics with real coefficients have solutions that occur in conjugate pairs.

Students and teachers will cover how to prove the conjugate root theorem — if \(z = a + ib\) is a root of a polynomial \(P(x) = 0\) with real coefficients then \(\bar{z} = a - ib\) is also a root — and how to use it to solve polynomial problems in the HSC Extension 2 course.