I have a Jensen TV, Model Number TS2050J. I need to know if it has a QAM tuner built in.

Hi.
No, your tv is an older model sdtv with an analog only NTSC tuner.

Newer model have an ATSC/Qam digital tuner, but not your model.

This means that if you want to watch tv, you'll have to get a converter box. It will have the ATSC/QAM tuner i it, and it converts the signal into lower definition NTSC, and then sends it to the tv through either coax cable, or rca cables.
Once in a great while you might even find one that has s-video output, but those usually are expensive.

I hope this helps you out.