1981 hsc (1 Viewer)

Bunzhou · Oct 26, 2009

Yeah I know how to do that part, those are the parts before this question which I don't know how to do (not sure if they're related......i think so) Question: Let α, β be real numbers.Find, in its simplest form, the cubic equation whoseroots are α + β,αω + βω^−1, αω^2 + βω^−2.

untouchablecuz said:
$P(z)=z^3-1\\P(w)=w^3-1=0\Rightarrow \omega^3=1\\P(\omega^2)=(\omega^2)^3-1=(\omega^3)^2-1=1^2-1=0\\\therefore \omega^2 \text{ is also a root of }P(z)$

1981 hsc (1 Viewer)

untouchablecuz

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Bunzhou

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