REMINDER: NOT A TEACHER
(1) You have already been given excellent answers.
(2) I just wanted to point out that although your first sentence (the one without the
relative pronoun "that") is now considered incorrect English, kindly remember that
in earlier English it was not that uncommon, among some speakers.
(3) So if you read such sentences, don't be too shocked.
(4) Here are some examples from the great George O. Curme in his masterpiece
A Grammar of the English Language:
I haue [have] a neece [niece] is a merchant's wife.
I bring him news will raise his drooping spirits.
It's the like of that talk you'd hear from a man would be losing his mind.
There's no investment in the world would give you a return like that.
Any man can't fight for his friends [had] better be dead.
(5) The good professor was writing about 80 years ago. At that time, he
says, such sentences were still popular among many speakers of Irish English and,
he adds, in the "mountain dialect of [the American state of] Kentucky."