Problem 39

Algebra Level 5

Consider an equation \(x^4+ax^3+bx^2+cx+d = 0 \) with roots (of \(x\)) \(x_1,x_2,x_3\) and \(x_4\). If \(x_1^{2016} + x_2^{2016} + x_3^{2016} + x_4^{2016} = 4 \), find the maximum value of \(a\), \(a_{\text{max}} \).

Submit your answer as \(a_{\text{max}} +b+c+d+x_1+x_2+x_3+x_4\) when \(a_{\text{max}} \) is fulfilled.


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