Finding Σα^2β from a quartic equation

I'd like to see what specific formulas you were taught; for example, is your work on (a) just applying a taught formula for the sum of squares, or did you derive it from other more basic formulas? Also, what does your Si notation mean?

Some sites just give formulas for all these things, while others might teach you a couple basic formulas (e.g. for sums of products of different numbers of roots) and let you apply those to different problems. If you need to learn the latter skill, then we need to know the facts that you have to work with, rather than just giving you another.
 
Yes, I am just applying a taught formula as I've learnt how to derive most of these, I'm only having trouble to derive the formula to obtain the answer for (e). My Sn notation is meant for the sum of roots such as (S1= alpha + beta + gamma, or S2= (alpha)^2+ (beta)^2 + (gamma)^2, etc.). These are some of the formulas I've been taught in the attachments below:
 

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Antroph1c said:
Yes, I am just applying a taught formula as I've learnt how to derive most of these, I'm only having trouble to derive the formula to obtain the answer for (e). My Sn notation is meant for the sum of roots such as \(S_1= \alpha + \beta + \gamma\), or \(S_2= (\alpha)^2+ (\beta)^2 + (\gamma)^2\), etc.). These are some of the formulas I've been taught in the attachments below:
Click to expand...
Thanks. What I see here is that you were shown how to derive formulas for [imath]S_n[/imath] from the fact that the coefficients easily give you [imath]\Sigma\alpha[/imath], [imath]\Sigma\alpha\beta[/imath], [imath]\Sigma\alpha\beta\gamma[/imath], and so on. The assignment asks you to first apply the provided formulas, and then to take it one step further by deriving your own formula for [imath]\Sigma\alpha^2\beta[/imath], which presumably can be obtained by similar thinking.

I'll just suggest a starting point. Just as they derive [imath]\Sigma\alpha^2[/imath] by combining [imath](\Sigma\alpha)^2[/imath] and [imath]\Sigma\alpha\beta[/imath], try thinking about [imath]\Sigma\alpha\cdot\Sigma\alpha\beta[/imath], because the terms of that product include the kinds of terms you need.
 
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