# Summation to Equation

Algebra Level pending

Consider $$f(x) = \sum\limits_{n=x}^{x^2} n$$ for all positive integers $$x$$.

It can be represented by a polynomial of degree four with complex roots $$a_1, a_2, a_3, a_4$$.

Evaluate the sum of the coefficients of $$g(x)$$ such that its roots are $$a_1^2, a_2^2, a_3^2, a_4^2$$.

×