Question 11
Consider all integer-coefficient polynomials $f(x)=(x-a_1)\cdots(x-a_{100})$, where all $a_i$ are real. Find the largest possible value of $\{a_1\}+\cdots+\{a_{100}\}$. Here $\{x\}=x-[x]$ and $[x]$ is the greatest integer not exceeding $x$.