Variation 2 · answer guide

Polynomial roots — Sum of zeros monic cubic

Question

Zeros of include and . The third zero is

This practice question was inspired by Question 1 in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: translate the requested symmetric expression into sums and products of roots from the coefficients.Sum of zeros : .
Finish the calculation, then check that the result meets the question’s conditions.Product: .
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Synthetic division by yields factor .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.