I have mobile iron on my mobile phone which is used to access company data on my phone. Does MDM also help in detecting and keeping away the malware from my phone?
I don't have experience with Mobile Iron, but I have used other MDM clients like AirWatch. They do not inherently give more protection or scanning for malware. MDMs are simply management solutions and remote administration (very limited in some cases) for devices the provider would like to issue resources and connections to. Some things may help, like requiring a password to install anything, and restricting the app stores - but, unpatched exploits like Quadrooter would still have an impact on you. Secure AV deployment would aid a bit in security, but as always is not a bulletproof methodology.