Lets look as Isaiah:
(Isa 11:1 And there shall come forth a rod out of the stem of Jesse, and a Branch shall grow out of his roots)
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(Isa 11:10 And in that day there shall be a root of Jesse, which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious.)
(Isa 11:11 And it shall come to pass in that day, that the Lord shall set his hand again the second time to recover the remnant of his people, which shall be left, from Assyria, and from Egypt, and from Pathros, and from Cush, and from Elam, and from Shinar, and from Hamath, and from the islands of the sea.)
Paul is quoting directly from Isaiah, the remnant was being gathered and the Gentiles were trusting in him.
(Rom 15:12 And again, Esaias saith, There shall be a root of Jesse, and he that shall rise to reign over the Gentiles; in him shall the Gentiles trust.)
Isaiah's prophecy came true in Paul's day, that's why he quoted Isaiah.