Definition of root for phrasal verb from the Oxford Advanced Learner's Dictionary

 

root for

 phrasal verb
phrasal verb
 
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Phrasal Verbs
[no passive] (usually used in the progressive tenses) (informal) to support or encourage somebody in a sports competition or when they are in a difficult situation We're rooting for the Bulls. Good luck—I'm rooting for you!
See the Oxford Advanced American Dictionary entry: root for