No way using a non-root account.
Here are some things to try:
1) If you have sudo access, try entering "sudo passwd root" from a command prompt. Enter your password once, then a new root password twice.
2) Boot into single user mode and you'll be root. Mount your root filesystem (mount / -o remount,rw), then use passwd to change the root password. Issue sync, then reboot. The way you get into single user mode depends on if you are using GRUB or LILO. It may not work on all distros. You can search the web for GRUB and LILO examples.
3) You can boot a rescue CD or a Linux install CD to a command prompt, it doesn't even necessarily need to be your current distro, then mount your root filesystem, then edit the /etc/shadow file to replace the current root password with the encrypted password string from an account that you know the password for.
Red Hat documents how to do item 2 above, assuming you are using GRUB.
https://access.redhat.com/site/docum...ot-passwd.html