when you boot into Linux, at boot time pass the kernel the option "1". for instance, if you use grub as a boot-loader, press "a" for command-line boot and write "linux 1". that will boot you up in runlevel 1, which is single user/maintenance mode. at this stage you will have root privileges without typing the password. then follow normal procedure for password changing.
ps: this can also work if you want to play a joke on your friends and change their root passwords.
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