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Hull City were relegated from the Premier League on Sunday after drawing 0-0 at home to Manchester United on a final day of the season marked by high-profile departures.
Hull, beaten FA Cup finalists last season, needed to beat United to stand any chance of staying up, but their failure to do so left them three points adrift of safety.
Newcastle United were the only other team at risk of relegation, but they secured their top-flight status with a 2-0 victory at home to West Ham United.
Jonas Gutierrez, who returned to action last month after a 17-month battle with testicular cancer, was Newcastle's saviour, teeing up Moussa Sissoko for a 54th-minute header and scoring with a deflected effort.
At Hull, Manchester United were without on-loan striker Radamel Falcao and injured goalkeeper David de Gea, heavily linked with Real Madrid, meaning both may have played their final games for the club.
The hosts made an enterprising start and saw Paul McShane and Dame N'Doye have goals ruled out for offside, while United goalkeeper Victor Valdes saved brilliantly from Ahmed Elmohamady.
The visitors lost Angel di Maria to injury and saw substitute Marouane Fellaini sent off for an ugly foul on McShane.
But home manager Steve Bruce, the former United captain, was unable to engineer a first managerial win over his old employers as Hull sank into the Championship.
Steven Gerrard scored in vain on a wretched final appearance for Liverpool as Brendan Rodgers's side sank to a humiliating 6-1 defeat at Stoke City.
With Raheem Sterling benched over his contract stand-off with the club, Liverpool conceded five first-half goals, with Mame Biram Diouf scoring twice and Jonathan Walters, Charlie Adam and Steven Nzonzi also on target.
Gerrard replied in the second half, to give the visiting fans one last goal before his departure for the Los Angeles Galaxy, but ex-Liverpool striker Peter Crouch restored Stoke's five-goal cushion late on.
Liverpool nevertheless qualified for the Europa League alongside Tottenham Hotspur, who won 1-0 at Everton courtesy of Harry Kane's 21st goal of the league campaign and 31st in all competitions.
Gerrard's former England team-mate Frank Lampard also found the net in his final game before leaving England for the United States, but he scored in a winning cause as Manchester City beat Southampton 2-0.
The 36-year-old midfielder, who is due to join New York City, converted a cross from James Milner in the first half at the Etihad Stadium, with Sergio Aguero scoring his 26th goal of the campaign in the 88th minute.
City's win condemned Southampton to seventh place, which will yield a Europa League spot if Arsenal beat Aston Villa in the FA Cup final on Saturday.
Another departing Premier League stalwart, Didier Drogba, was carried off the pitch by his team-mates after injuring himself in the early stages of Chelsea's 3-1 win at home to Sunderland.
At that point, the champions trailed to a 26th-minute Steven Fletcher header, but after Diego Costa, Drogba's replacement, equalised with a penalty, Loic Remy scored twice in the second half.
Arsenal rubber-stamped third place by demolishing West Bromwich Albion 4-1 as Theo Walcott staked a strong claimed for a cup final place with a first-half hat-trick.
The England forward, whose season has been disturbed by injuries, scored three times in 33 minutes, with Jack Wilshere also on target. Gareth McAuley replied for West Brom.
Villa will go into the cup final on the back of a defeat after a first-half Danny Ings header saw them beaten 1-0 at relegated Burnley.
Leicester City celebrated their stunning escape from relegation with a 5-1 romp at home to relegated Queens Park Rangers, who finished the season bottom of the table.
In the day's other game, Crystal Palace beat Swansea City 1-0 courtesy of a 57th-minute goal by Marouane Chamakh.
Sunday's results:
Arsenal 4-1 West Bromwich Albion
Manchester City 2-0 Southampton
Everton 0-1 Tottenham Hotspur
Leicester City 5-1 Queens Park Rangers
Crystal Palace 1-0 Swansea City
Newcastle United 2-0 West Ham United
Chelsea 3-1 Sunderland
Hull City 0-0 Manchester United
Aston Villa 0-1 Burnley
Stoke 6-1 Liverpool
