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Polynomial with roots which are the squares of another polynomials roots

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frog0101:
Hi,
For a question such as 2016 HSC Q15 (a), given the polynomial,
, find a cubic equation with integer coefficients that has roots .

If I approach the question:

RuiAce:
Note how the question says "find a cubic equation" and so on. Because we only want one cubic equation, which is what they'll typically always do, we can just take the positive root for convenience.

It turns out that there's gonna be more than one cubic equation that works in general (in fact, up to 8 of them). If we wanted to "find all cubic equations", then the computations would be more demanding and require the cases that you've considered.

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