Discriminant vs Graphs

Algebra Level 2

\[\begin{array}{} f(x) &=(x-a)(x-e)\\ &+ \ (x-b)(x-f) \\ &+ \ (x-c)(x-g) \\ &+ \ (x-d)(x-h) \end{array}\] 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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