Talk:A-level Mathematics/OCR/FP1/Roots of Polynomial Equations

Characterization of symmetric polynomials is incorrect
The current characterization of symmetric polynomials is incorrect. A symmetric polynomial (in more than one variable) is one which is invariant under a permutation of the variables. For example $$x+y = y+x$$ is a symmetric polynomial in $$x$$ and $$y$$.

It doesn't tell us very much to say a particular polynomial in the single variable $$x$$ is symmetric, because all polynomials in one variable are. Indeed, this means that the claim that 'the polynomial $$4x^3 + 12x^2 - 7x - 30$$ is not symmetrical' is false.

The relevant discussion of symmetric functions is to do with the fact that if, say, $$\alpha, \beta, \gamma$$ are roots of a cubic equation, then the quantities like $$\alpha + \beta + \gamma$$ in which we are interested are themselves symmetric in $$\alpha, \beta, \gamma$$. --Onygo (discuss • contribs) 15:42, 8 January 2018 (UTC)