Zeros of a Polynomial

Zeros of a polynomial is part of the Complex numbers topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-03). This subtopic uses complex numbers to factor polynomials completely, so that a polynomial of degree \(n\) has exactly \(n\) complex zeros, including factoring sums of squares using \(i\).

Students and teachers will cover how to factor a polynomial all the way to linear factors over the complex numbers, list all of its zeros, and use the relationships between roots to solve problems — extending real factorising to the complex numbers in the HSC Extension 2 course.