Support · Mathematics Extension 2 11–12 – Year 12 · Introduction to complex numbers
Support Prove the complex conjugate root theorem: if the complex number z = a + ib is a root of the polynomial equation P(x) = 0 with real coefficients, then the complex conjugate z̅ = a - ib is also a root of P(x) = 0
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
State the multiplicity of each root of a polynomial equation given in factored form
Mathematics Extension 1 11–12 – Year 11 · Polynomials Draft mapping
No checked resources on this prerequisite dot point yet.
Express the result of the division also in the form (P(x))/(A(x)) = Q(x) + (R(x))/(A(x))
Mathematics Extension 1 11–12 – Year 11 · Polynomials Draft mapping
No checked resources on this prerequisite dot point yet.
Prove that if a cubic P(x) = ax³ + bx² + cx + d has three zeroes α, β, γ, then α + β + γ = - b/a, αβ + βγ + γα = c/a and αβγ = - d/a
Mathematics Extension 1 11–12 – Year 11 · Polynomials Draft mapping
No checked resources on this prerequisite dot point yet.