Stratix4GX PCIe development board to used as root port

I would be surprised if you can put a root port on a PCIe expansion card handled by a root port on the motherboard, so the answer is: No, it’s not possible.

As written, the only way to make use of a root port in an FPGA is to drive another end point, or a switch with multiple end points behind it, when connected properly using such a dev kit with a PCIe socket card. Or you can build your own motherboard.

edit:

Maybe you meant something different? You don’t have to be a root port to send out requests on PCIe, but you have to have OS driver support to have proper I/O to I/O communication between your device and another end point. Most of the time it’s easier to let the devices communicate just with the main processor behind the motherboard root complex which then orchestrates data transfers using OS drivers. Only very high I/O rates or low-latency applications require direct device-to-device communication.