quadratics with related roots

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?

--
Adam Atkinson
ghira@xxxxxxxxxxxxx

.

Relevant Pages

  • Re: quadratics with related roots
    ... >> formulas involving alpha and beta), ... >> and beta. ... >> I did maths at university and don't recall ever having do to anything ... manipulate roots of polynomials without ever knowing the value of them. ...
    (sci.math)
  • Re: quadratics with related roots
    ... > If the roots of the quadratic equation are ... > formulas involving alpha and beta), ... > I did maths at university and don't recall ever having do to anything ...
    (sci.math)
  • Re: quadratics with related roots
    ... > If the roots of the quadratic equation are ... > formulas involving alpha and beta), ... > I did maths at university and don't recall ever having do to anything ...
    (sci.math)
  • Re: quadratics with related roots
    ... > are alpha and beta, write down a quadratic whose roots are (two ... denoted by say C_1 and C_0 resp, which are symmetric polynomials ...
    (sci.math)
  • Re: Sphere packing in six dimensions, root system for E6, Wikipedia article
    ... in Phi_E8 with alpha and beta orthogonal, ... counting orthogonal roots as usual. ... "Essays in the history of Lie groups and algebraic groups", ...
    (sci.math)