Looking at recommendations for a graphics card that fulfills the following spec in order of importance:
- Dual 4K (60hz) capable
- Passive cooled
- Cheap (only business graphics required)
- Two displayport/ mini display port connectors
- AMD chipset
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The issue is that two displays in 4K is only supported (from what I know and at the moment) by gaming cards... So in this case, you can forget cheap, passive etc. X)
However, did you consider using 2 GPU? The Radeon R7 250 passive (~70€) can display in 4K. In this case, 2 GPU isn't that expensive and will support 2 displays.
AMD Fury X
It has the ports, its kind of passive cooled.. comes with a built in AIO cooler. Cheap is a relative term. The fury x is around 600$, but I'm sure there are cheaper models.
So I'm a nvidia guy, and I don't have a way of testing it but I'm sure my 970gtx can push 2x 4k office sessions. And that gpu is only 300$ It's currently pushing 3 1080p displays without so much as breaking a sweat during gaming. If you like to join forces with the green team, there are plenty of options over here.
I'll recommend a card based on the newly released Polaris architecture. The RX 470 seem to fit your needs nicely, considering you don't plan on gaming.
The reference version has 3 DP and 1 HDMI output. Unfortunately, since it is a gaming card, it is unlikely to be passively cooled, however, most 3rd party cooler designs will be semipassive, which switches off the fans at low load, which is almost as good. They are still very quiet, potentially much quieter than your case fans.
Since the TDP is only 100 W, you could also get a high end passive cooler, such as the Accelero S3 for an extra USD 55, provided you're willing to install it yourself.