I was attempting this tutorial question:
a) For each of the following sets, decide whether it is representable as a polyhedron.
(ii) The set of all $x \in \mathbb{R}$ satisfying $$x^2 − 8x + 15 \leq 0$$
The corresponding answer was :
(ii) The second set can be expressed as $x \in \mathbb{R}$ satisfying the two linear constraints $x \geq 3$, $x \leq 5$. Hence it is representable as a polyhedron.
This result puzzled me. My current understanding is the set satisfying $ x^2 - 8x + 15 \leq 0 $, $x$ can be expressed as the set in $ \mathbb{R}$ satisfying $ x \geq 3 $ and $ x \le 5 $. However, this corresponds to the curved region of the quadratic region which has an infinite number of points. To my understanding, in a polyhedron, there are only a finite number of vertices.
Just wondering if anyone could help me clear my misconceptions.