Luckily this is extremely easy to do and just takes about 20 seconds.
Here are the steps to change your root password.
Step #1) Install MobileTerminal
Open Cydia and go to search on the bottom right, type MobileTerminal. Download the one that looks like this MobileTerminal(NEW)
Step #2) Log in to your iDevice.
To do this we type the command, su root.
Step #3) – enter you password
By default your password is alpine, so type alpine
Step #4) – Enter the command to change your password
To do this, type: passwd. (No o, or r.)
Step #5) – Enter a new password
Step #6) – Confirm your new password
Step #7) – You are done! Good job.
Click here for a video of how to change your root password on your iDevice.