Final answer:
The objectives President Bush named were to bring terrorists to justice and preventing those seeking WMDs from threatening the US, leading to the invasions of Afghanistan and Iraq under the Bush Doctrine.
Step-by-step explanation:
The two great objectives that President Bush named in response to the terrorist attacks on September 11, 2001, were bringing terrorists to justice and preventing those who seek weapons of mass destruction (WMDs) from threatening the United States. In his address to the nation, Bush emphasized the need to shut down terrorist camps, disrupt their plans, and bring them to justice, as well as to fight against those harboring intentions to develop and use WMDs against the United States. This stance was a part of the Bush Doctrine, which justified pre-emptive wars and the ousting of hostile regimes to establish friendly and democratic governments in order to protect U.S. national security. The subsequent invasion of Iraq was defended by the administration as a necessary measure against Saddam Hussein, who was believed to be developing such weapons and potentially aiding terrorist groups like Al Qaeda.