Summation to Equation

Algebra Level 4

Consider the polynomial representation \(h(x)\) of \(f(x) = \sum\limits_{n=x}^{x^2} n\) for all positive integers \(x\).

If \(h(x)\) has complex roots \(a_1, a_2, a_3, a_4\), then evaluate the sum of the coefficients of the monic quartic polynomial \(g(x)\) possessing roots \(a_1^2, a_2^2, a_3^2, a_4^2\).

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