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TASSpecialist MathematicsQuick questions
Unit 3
Quick questions on Factorising polynomials over the complex numbers - TCE Mathematics Specialised (Tasmania)
3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is the conjugate root theorem?Show answer
The reason is the conjugate arithmetic from earlier work: taking the conjugate of the whole equation replaces each by but leaves the real coefficients unchanged, so as well. A practical consequence is that real polynomials of odd degree must have at least one real root, because complex roots are used up in pairs.
What are real quadratic factors?Show answer
A conjugate pair of roots corresponds to the real quadratic factor
What is factorising a given polynomial?Show answer
When you are handed a polynomial and one complex root, divide out the corresponding real quadratic, then factor the remaining quotient.
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