You can either extract your own pomegranate juice with a juicer or buy pomegranate juice at your local grocery store.
Roast the vegetables: Preheat oven to 425 degrees. Toss together vegetables and oil in a large bowl, and season with salt and pepper. Spread vegetables evenly on 2 rimmed baking sheets, and roast until golden, mixing halfway through, about 30 minutes.
Meanwhile, make the vinaigrette: Transfer pomegranate juice to a bowl. Pour in oil in a slow, steady stream, whisking until emulsified. Season with salt and pepper.
Just before serving, drizzle vinaigrette over warm vegetables, and toss with pomegranate seeds.