MHB What are the requirements for the exercise on multiplicity and set of zeros?

[forever119]

 

[Opalg]

Hi forever119, and welcome to MHB.

For that exercise, there seems to be no need for $f(a)$ and $f(b)$ to be nonzero. It looks as though that requirement is only needed for the following exercise, which refers to the signs of $f(a)$ and $f(b)$. These need to be strictly positive or strictly negative for that exercise to make sense.