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I am going through Wikipedia's solution of a quartic equation and have got stuck with notation in the solution. The solution is given by this equation:


What is confusing me is the significance of the following two symbols weird symbol and weird symbol 2. Can anyone explain what they mean please? I apologise for the relative simplicity of the question.

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up vote 5 down vote accepted

It says:

Note: The subscript $s$ of $\pm_s$ and $\mp_s$ is to note that they are dependent.

It also says:

Remember: The two $\pm_s$ come from the same place in equation (7'), and should both have the same sign, while the sign of $\pm_t$ is independent.

Thus, in other words, these symbols give you a convenient way of writing down all four solutions in a single formula. Those four solutions are characterised by the choice of signs in the formula; there is $\pm_s$ and $\pm_t$, which are independent, and hence together give you 4 choices: $(\pm_s, \pm_t) =(+,+), (+,-), (-,+)$ and $(-,-)$.

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sorry, I still do not understand. – Adrien Hingert Jan 26 '12 at 16:28
I've added further explanation; is it clearer? – Rick Jan 26 '12 at 16:31
Yup, thanks, very clear now! – Adrien Hingert Jan 26 '12 at 16:33
One last thing: as the +/- on the t is inverted, does this mean it has to have the opposite signe of the "s"? – Adrien Hingert Jan 26 '12 at 16:36
As a standalone formula, whether $\pm_t$ is inverted or not is immaterial (because it appears only once in the formula). The reason, it seems, that the formula you cite reads $\mp_t$ is because the article derives that formula from a previous equation, so the authors supposedly wished to preserve the correspondence between the roots. – Rick Jan 26 '12 at 16:43

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