Reading rooms must-----quiet.

需要,因为这里有must,注意体会.
不过,英语中有些动词能以主动表示被动意义:
The cloth washes well.
The door won't lock.
The pen writes smoothly.等等
这种句子的主语常是"物",且此物常具有某种内在的特点,使动词所表示的动作得以实现或难以实现,因此主语可以看作动作的执行者,如改为被动,意义有所区别,如:
His novels don't sell.(销路不好)
His novels are not sold.(与小说本身无关,小说可能不错,但未售出)