Isaiah 11-12 is a messianic and eschatological prophecy. It begins by identifying the king.1
There shall come forth a shoot from the stump of Jesse, and a branch from his roots shall bear fruit. (Isaiah 11:1 ESV)
ויצא חטר מגזע ישי ונצר משרשיו יפרה
The king is identified using two terms, גֶּזַע and שֶׁרֶשׁ. גֶּזַע is only used three times in the Old Testament: here, Isaiah 40:24, and Job 14:8. the exact meaning is debatable. The second term means "root."
The Rod from the "stump" of Jesse would identify the future king as a descendant of David. The Branch from the "root" seemingly looks back in time to who established Jesse. As a way to identify a single ancestor from Jesse, this double identification seems unnecessary. On the other hand the two-fold description could identify two: one descended from Jesse and one from before Jesse.
Based on the LORD's selection of David "...I have provided for myself a king among his sons.” (1 Samuel 16:1) the "root of Jesse" might be taken as a divine entity, not as a reference to David.
The LXX eliminates the first term and uses ῥίζα, "root" for both:
And a rod shall come out of the root of Iessai, and a blossom shall come up out of his root. (LXX-Isaiah 11:1 NETS)
καὶ ἐξελεύσεται ῥάβδος ἐκ τῆς ῥίζης Ιεσσαι καὶ ἄνθος ἐκ τῆς ῥίζης ἀναβήσεται
By placing the sole emphasis on the second means of identifying the future king, it seems as if the intention is to heighten the messianic focus of the passage, and by eliminating the first reference to a Davidic figure, envisions a divine Messiah.
Is the "root of Jesse" in the LXX, a reference to a divine Messiah?
1. Benjamin D. Sommer, The Jewish Study Bible, Edited by Adele Berlin and Marc Zvi Brettler, Oxford University Press, 2004, p. 807