2025 HSC Mathematics Extension 1
Question 11(f):
Polynomial roots
The roots of are . Find .
How to recognise this question
Question type: polynomial roots
- The command and notation point to polynomial roots.
- The requested response is a worked solution.
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 , the sum is and product is .
- The required value is .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks 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 roots of are . Find .
Question 2
Find the monic cubic whose roots are , and .
Question 3
If are roots of , find .