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England managed to avoid the follow-on with Root and Stuart Broad trying to revive their team's attack, but after an impressive showing, Broad was dismissed just shy of his half-century.
Bhuvneshwar Kumar managed to send Broad packing for an lbw, which was met with a chorus of boos from the Trent Bridge crowd, but replays showed that the ball would have hit leg stump.
Broad, who hit 47 from 42 balls, was shortly joined in the pavilion by Liam Plunkett, who was bowled out by Kumar having reached just seven runs.
With one wicket remaining, Root tried to keep the attack going by reaching 50, his fifth in Test format, while Anderson unleashed numerous reverse sweeps after entering the field.
However, there was an injury concern for Anderson after the ball smashed onto the top of his right hand, which required treatment from the physio, but he was able to continue.
Both Root and Anderson remain unbeaten on 78 and 23 respectively, while England trail by 105 runs.