The most effective method for eradicating a rootkit from an infected system is to format the drive, reinstall the operating system, apply any applicable patches, and change all passwords. Rootkits are designed to be deeply embedded within the system, making them difficult to remove completely via conventional means such as uninstalling or deleting specific files. Formatting the drive ensures that all malicious software is removed, and reinstalling the OS ensures a clean and secure system environment. Changing passwords afterward is crucial to prevent reinfection or unauthorized access.