This is one of the 117 mis-spellings listed as 'Common difficulties' in the section on 'Spelling' within 'Writing' in UEfAP.
Although loose pronunciation sometimes reduces deteriorate to four, or in the extreme three, syllables ('deter'[i]ate'), it properly (in RP) has five: 'di-TEER-i-or-ate', IPA: /dɪ ˈtiːr ɪ ər reɪt/. The spelling reflects this: deteriorate. To miss out either of the middle syllables (
deterorate or deteriate) indicates carelessness.