First and foremost, are you sure it is the right password? Remember they are case sensitive, so if you mistype anything, it will not connect.
Also, have you tried restarting the tablet and seeing if it will connect after?
If you are putting the correct wifi password, and it gives you the authentication failed to connect, you can try the following...
1. Log into your wireless modem/router, via the computer you have using it's device IP address.
If you are not sure of the ip address, you can get it through google. Just type "my ip" in google search and it should show you the address.
2. Next make sure wireless security mode setting is set to "wpa/wpa2-psk" on the modem/router. If it isn't, set it to that setting and click "apply".
3. If it's set to wpa/wpa2-psk then it's probably a hardware issue with your modem/router.
This will, however, only work if the modem/router is yours to access.