In the race for the 2020 Democratic presidential nomination, former Vice President Joseph R. Biden holds a 10-point lead over Sen. Elizabeth Warren in Texas, according to a Quinnipiac University poll released on Wednesday.

Mr. Biden was the top choice of 28% of Democrats and Democratic-leaning independents, followed by Ms. Warren of Massachusetts at 18% and Sen. Bernard Sanders of Vermont and former Rep. Beto O’Rourke of Texas at 12% apiece, according to the poll.

“Senator Warren’s popularity continues to grow in Texas as well as nationally. But in either case, the changes are small, and Biden holds on to his double-digit lead,” said Quinnipiac University Polling Analyst Peter A. Brown.

Sen. Kamala D. Harris of California was at 5%, Mayor Pete Buttigieg of South Bend, Indiana and former housing secretary Julián Castro were at 3% apiece, and Sen. Amy Klobuchar of Minnesota was at 2%.

Fifty percent of respondents said Mr. Biden has the best chance of beating President Trump, compared to 10% apiece for Ms. Warren and Mr. Sanders.

But 31% said Ms. Warren has the best policy ideas, and she was followed by Mr. Biden at 15% and Mr. Sanders at 13%.

“In Texas, the stereotype holds that Sen. Warren is the candidate of Democrats’ hearts — they say two-to-one she has the best ideas — while Biden is the candidate of Democrats’ heads, with a five-to-one lead over Warren when it comes to who has the best chance to win against Trump,” Mr. Brown said.

Among all registered voters, President Trump had a 45% job approval rating in the state, compared to 50% who said they disapprove. Nearly half — 48% — said they definitely would not vote for Mr. Trump is he was the Republican nominee, compared to 35% who said they would definitely vote for him and 14% who said they would consider voting for him.

The overall survey of 1,410 self-identified registered voters in the state was taken from Sept. 4-9 and has a margin of error of plus or minus 3.1 percentage points.

The subsample of 456 Democrats and Democratic-leaning independents has a margin of error of plus or minus 5.5 percentage points.

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