2024 HSC Mathematics Extension 1
Question 1:
Polynomial roots
The polynomial has zeros , and .
What is the value of ?
How to recognise this question
Question type: polynomial roots
- The command and notation point to polynomial roots.
- The requested response is a multiple choice.
How to handle it: translate the requested symmetric expression into sums and products of roots from the coefficients.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- For a monic cubic with zeros , the product of zeros satisfies .
- Here , so .
- Alternatively expand and match the linear coefficient, or use sum of zeros: .
- Check: .
- Answer: B. (NESA multiple-choice key: B.)
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
The polynomial has zeros , and . What is ?
Question 2
Zeros of include and . The third zero is
Question 3
If has zeros , and , then equals