Re: quadratics with related roots

In article <1118757203.118951.256150@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Adam Atkinson" <ghira@xxxxxxxxxxxxx> wrote:

> I've been helping someone with maths, and some things have cropped
> up which I remember seeing at school but have never used or seen since.
>
> One particular item I'm curious about is questions of the form:
>
> If the roots of the quadratic equation (insert quadratic here) are
> alpha and beta, write down a quadratic whose roots are (two
> formulas involving alpha and beta), without solving for alpha
> and beta.
>
> I've seen cases like asking for roots alpha^2 and beta^2
> or alpha/beta and beta/alpha.
>
> I did maths at university and don't recall ever having do to anything
> like this. Is there some field of maths, science or engineering in
> which people need to produce equations with related roots like this?

It comes up from time to time in Algebraic Number Theory
and/or Galois Theory, but mainly I think it's there as
a good question to test whether a student really understands
what's going on.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

Relevant Pages

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