Does HD video camera + Regular DVD burner + HDTV = Bad picture?

Here’s the scenario: I have a Sony HD video camera and just purchased a regular DVD burner to store the HD videos. My question is, “will the DVD’s look bad when played on a High-Def Television?” (I don’t have an HD television yet, or I would just try it). I’m wondering if I wasted my money on the regular DVD burner. I just read somewhere that Blu-ray burners are the only thing that looks good on an HDTV and that a regular DVD will look bad.