The poll shows the president's approval rating jumping 5 points, from 35 percent to 40 percent, from earlier this month.
"With only a slight bombing bump, President Donald Trump stays mired in miserable numbers", Quinnipiac pollster Tim Malloy said.
According to Gallup, 52% of Americans disapprove of Trump.
First Daughter Ivanka Trump has a positive 36 - 31 percent favorability, but voters say 53 - 36 percent that it is not appropriate that she play a "significant role in the White House".
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Sixty-one percent support his missile strike against Syria almost two weeks ago, but 62 percent believe that it will not deter the Syrian government from using chemical weapons in the future.
Some female members of the Trump family do better than the president.
Trump dropped to 42% eight days after taking office.
By comparison, the latest CBS News survey, released last week, found Mr. Trump's approval rating at 43 percent and his disapproval at 49 percent.
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Is it about Joe Hart? I think that's important for all of us, to understand and accept his advice and plans. The young ones have made really big steps, Caoimhin Kelleher and Kamil Grabara, and that is really good.
However, 39 percent of voters did give him good marks when asked how he was handling the economy and job creation.
USA has "moral responsibility" to get involved: 52 percent.
First Son-in-Law Jared Kushner gets a negative 15 - 32 percent favorability rating, with 50 percent who don't know enough about him to form an opinion of him.
USA should not get involved: 40 percent. Voters disapprove of his work thus far on immigration by a 58-39 margin, and and 61 percent disapprove of his handling of the environment.
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The Quinnipiac poll surveyed 1,062 voters nationwide between April 12 and 18, and it has a margin of error of plus or minus three percent.