90% of Android devices are safe from QuadRooter exploits thanks to Google's Verify Apps
Since Verify Apps is enabled by default on devices running Android 4.2 or later and featuring Google Play services, it safeguards about 90% of all Android devices currently in use. If you do try to install content from unknown sources, Verify Apps will block the installation if it detects something suspicious. According to Android Central, Google confirmed that its protection features will "identify, block, and remove applications that exploit vulnerabilities" like QuadRooter. To make your device exposed to QuadRooter, you'd have to manually disable Verify Apps - but that's not advisable in any scenario.
Things that are NOT allowed: