What might happen if you put a Polar Bear and a penguin into the same enclosure in a zoo?

A Polar Bear would eat the penguin.
Polar Bears would normally eat fish and seals.

Penguins, like all birds, are built to escape from large terrestrial or aquatic carnivores. In penguins case: by swimming faster away from them or by swimming towards land and then walking away. Birds are not and were never as heavily built as large terrestrial megafauna like mammals, reptiles, or non avian dinosaurs

If the bear was fed, they'd ignore each other.

You already know the answer to this question. An intelligent person would.

The penguin would become a light snack for the polar bear.

Here in the UK you would have committed a criminal offence in the process.

The penguin will become polar bear dinner.