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I happen to give some private lessons to an IB (International Baccalaureate) student. He asked me for help with writing some kind of a project on a set topic, given some materials (containing the definition and a few clues/overall plan of the paper). (Just in case someone is wondering: please notice that I do understand that "help with writing" is different from "writing it for someone", and I am very careful about only guiding him, but not doing his homework.)

My question is: where can I find some information (just basic things, definitions and maybe fundamental properties) about shadow functions? From the materials he was given (of rather medium quality, I'd say) I know that they can be applied to finding complex roots of some polynomial $P$ (seemingly with real coefficients) by means of associating with it another one (say, $S$), with only real roots (but connected with the complex ones of $P$: if $P(a\pm bi)=0$, then $S(a\pm b)=0$). Also, any kind of intuition would be helpful, but I specifically ask not to give any in the answer to this question; I prefer to find it myself from the definition and properties, please do not spoil my pleasure of finding it myself; if in trouble, I'll ask about it in another question.

As to the form: websites are fine, books too (my faculty has quite a decent library), I have also access to some journals (I imagine that a few of them, like, say, American Mathematical Monthly might contain some info), so please share any sources you know.

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    But how do you find the equation of the shadow fundtion?2012-03-22
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    What is a shadow function?2012-03-22
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    Well, I gave what I suspect is (more or less) the definition in my question (S would be the shadow function of P, in this case). But I'd like exactly to know whether my suspicion is correct, and maybe some additional background.2012-03-23
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    what is quartics' shadow function?2012-10-01

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