$\begin{aligned}
f(x) &= (x-a)(x-e)\\
&+ \ (x-b)(x-f)\\
&+ \ (x-c)(x-g)\\
&+ \ (x-d)(x-h)
\end{aligned}$
For real numbers $a<b<c<d<e<f<g<h$, we define the function as above. Then what can we say about the roots of $f(x) = 0$?

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