Which of these two sentences is correct?

Neither is correct, because you're using "one" as a noun which means you need the adjectives to modify it, "pessimistic" and "optimistic".

You can say:

It shows the life of two men, a pessimistic one and an optimistic one.

But I would use:

It shows the life of two men, a pessimist and an optimist.

or (a little fancier)

It shows the life of two men, one a pessimist and one an optimist.

2

It shows the life of two men, a pessimist and an optimist

that is correct

Neither. Try

It shows the life of two men, a pessimist and an optimist. OR

It shows the life of two men, a pessimistic one and an optimistic one.

I prefer the first, but both are OK..

I don't think either would normally be used by someone who speaks English as their first language. They would probably be more likely to say 'It shows the life of two men, a pessimist and an optimist'. Hope that helps

You don't need the word ONE.

It should be "It shows the life of two men, a pessimist and an optimist."

If you must use the word 'one' it would be..

"It shows the life of two men, a pessimistic one and an optimistic one."

You dont need to use the word 'ONE'

Its just: 'A pessimist & an optimist'

They are wrong -- as most everyone else stated. A double negative in a sentence doesn't really equal a positive, but those of us who are particular on the grammer we use, will often answer with --- "oh, then you want me to go?" or "what do you have?" Just don't use them, or people will think you to be iliterate. I ain't not got nothing more to say on this one . . . . UGH.

#2

number 1 but forget the (one ) at the end