After the tet offensive, how did the united states hope to end the vietnam war?

The Tet Offensive was a surprise attack launched by the North Vietnamese on the South during the Lunar New Year.  They were able to penetrate the capital and fighting spilled into the streets.  The U.S. embassy was broken in but the Americans managed to repulse the attack.  It was military victory or from the Americans but a political victory for the North.  American opinion turned against the war and later the Americans withdrew.

the roman army grew in size and became dominant in the mediterranean region.

the answer is false.