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Jadeja sustained a hamstring injury while K L Rahul has complained of pain in right quadriceps.
Hartley's 7/62 on his debut wrecked India, who were all out for 202 in an extended final session on the penultimate day.
Rehan Ahmed was keeping Pope company with England finishing the third day on 316/6, putting them 126 ahead.
The Indian pacer came up with a brilliant spell in the post-lunch session on the third day of the Hyderabad Test.
Ben Stokes produced a captain's knock of 70 to help England post at least a competitive total before they wilted early into the final session.
Root also inscribed his name in World Test Championship history by becoming the first batter to breach the 4,000-run mark.
India have won four out of the five Tests played at the Rajiv Gandhi International Cricket Stadium in Hyderabad, with one match ending in a draw.
The Uttar Pradesh wicketkeeper batsman is part of Rohit Sharma-led 16-member squad.
Shubman Gill has also been included in the three-match series beginning January 11.
The victory will act as a soothing balm for Rohit Sharma after the heartbreak in the World Cup final and the crushing defeat in the series opener.