"Los utilizan para mostrar lo negativo."
Translation:They use them to show the negative.
Lo is used as a direct object pronoun for masculine nouns and for cases where the gender is irrelevant/unknown. La is for feminine nouns.
'Él lo quiere' = 'He wants it'
'Lo' is used in this case because 'negativo' is actually an adjective, and when you use adjectives without nouns you have to have a pronoun.
'Lo peor ha pasado' = 'The worst has happened.
The only time you can use 'el [adjective]' is if there is a noun following this. The noun can however be implied, as in,
'Vivo en el tercero [piso]' = 'I live on the third [floor]'
Here's a link: http://spanish.about.com/od/nouns/a/adjective_noun.htm
From what I understand of Zikosi's explanation, "negativo" is an adjective, so the Spanish isn't saying "the negative", it's saying something like "showing it [to be] negative", where the "lo" is the "it".
Edit, weeks? later: Ok, I was wrong here. It is saying "the negative".
Yes, they could both be used. "Ustedes" can be implicit. This article is useful: http://spanish.about.com/od/pronouns/a/subject_pronoun.htm
Usually duolingo allows any English pronoun that fits the verb form.