(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the values of Σ(a^2), Σ(1/a), Σ(a^2)(B^2) and ΣaB(a + B) for: x^4 - x^3 + 2x + 3 = 0

2. Relevant equations

Σa = 1, ΣaB = 0, ΣaBC = -2, aBCD = 3

3. The attempt at a solution

I found the Σ(a^2) and Σ(1/a) successfully correct bt could neither find Σ(a^2)(B^2) nor (Σa)(ΣaB):

'ΣaB(a + B) = 6' is given as the answer but my own answer comes 4. Please somebody post the complete solution for ΣaB(a + B) explaining each step, given that i found ΣaB(a + B) = (Σa)(ΣaB) - 2(ΣaBc).

It seems i should have got ΣaB(a + B) = (Σa)(ΣaB) - 3(ΣaBc) in order to get the correct answer '6' instead of the erroneous '4'.

If perhaps this is true, then prove that ΣaB(a + B) = (Σa)(ΣaB) - 3(ΣaBc)

I found Σ(a^2)(B^2) = (ΣaB)^2 - 2Σ(a.B^2.C) - 4aBCD. Now 4m here i can't proceed forward to find Σ(a.B^2.C). Perhaps, i hav done it wrong or there exists an alternative easier way.

NB: a,B,C,D represent the roots alpha, beta, gamma and the 4th root (partial derivative sign) respectively.

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# Homework Help: A level Further Pure Maths help (Polynomials)

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