"PCI express 2.0 has a peak speed of 8 GB/s. 3.0 has a peak speed of 16 GB/s. ... PCI Express cards are backwards compatible, a modern PCI Express 3.0 graphics card will work in a motherboard with a PCI Express x16 2.0 slot "
"Yes. PCIE 2.0x16 card will work with PCIE 3.0 x 16 slot. But PCIE 2.0x16 card can work only at a max speed of Gen2(5.0GT/s). It can't work at Gen3(PCIE 3.0- 8 GT/s) speed even though the slot(Root complex) support Gen3. "