# "Sum" of the functions are interesting

Algebra Level 3
• $$f_k (x)$$ has three roots and they are $$k$$, $$-k$$ and $$0$$, where $$k$$ is a real positive integer $$\geq 1$$. Which of the followings (in terms of $$n$$) is the value of $$x$$ when$$f_1 (x)+f_2 (x)+\cdots+f_n (x)=0$$?
• Assume all $$f_k (x)$$ has equal real constant $$d$$, such that $$f_k (x)=d(x)(x-k)(x+k)$$ where $$d$$ is not $$0$$
• Given that $$x>0$$ and $$n=24$$,
• express your answer in the form $$\dfrac{a \sqrt b}c$$, where $$a,b$$ and $$c$$ are positive integers with $$a,c$$ coprime and $$b$$ square-free.

Submit your answer in the form $$a+b+c$$.

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