# 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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