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# Roots of polynomials

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1. http://filestore.aqa.org.uk/subjects...2-QP-JUN12.PDF

Is there like a quick, simple way to do part d? My method is long..
2. (Original post by Bobjim12)
http://filestore.aqa.org.uk/subjects...2-QP-JUN12.PDF

Is there like a quick, simple way to do part d? My method is long..
The original cubic is , these have roots . So the mapping has roots .

Specifically:
3. (Original post by Zacken)
The original cubic is , these have roots . So the mapping has roots .

Specifically:
ooh, that's what the mark scheme was doing ok,

so if the new roots were like ( 1 +2a), (1 +2b)....

you replace z with (1 +2z)?
4. (Original post by Bobjim12)
ooh, that's what the mark scheme was doing ok,

so if the new roots were like ( 1 +2a), (1 +2b)....

you replace z with (1 +2z)?
Eh, that makes too much of a mess. Easier to work with sums and product of roots in that case.
5. (Original post by Zacken)
Eh, that makes too much of a mess. Easier to work with sums and product of roots in that case.
ah ok, so my method, right, thanks
6. (Original post by Bobjim12)
ah ok, so my method, right, thanks
Yep! No problem.
7. (Original post by Zacken)
The original cubic is , these have roots . So the mapping has roots .

Specifically:
That's actually really useful to know before my exam on Friday, but at what point would you not bother with this? I understand as a replacement is pretty straightforward with these roots but are there any other combinations where this works with ease such as . Would test this right now but don't have much time. Thanks for the info though

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