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Variation 3 · answer guide

Quadratic inequality — Shifted roots outward

Question

Which diagram best represents the solution set of ?

Choose the number-line diagram that represents the solution set.
Choose the number-line diagram that represents the solution set.

    This practice question was inspired by Question 1 in the 2020 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

    Step by step

    1. Set up the solution: factor the quadratic, identify its roots, then use the sign of the quadratic on each interval.Factor: .
    2. Simplify the previous line carefully, keeping exact values where possible.Include endpoints for .
    3. Finish the calculation, then check that the result meets the question’s conditions.Non-negative outside: or .
    4. Match the result to the choices and state the correct option.Therefore option C is correct.

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

    Verification: Test (false) and (true); endpoints work.

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

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