Dear Customer,
HP does not provide Windows 10 drivers on HP.com for HP computers sold prior to August 2013. Microsoft has made most of the component drivers for these products available via Device Manager once the product is running Windows 10 with an active Internet connection. To see if your HP computer was tested to work in Windows 10, go to Upgrade to Windows 10 (in English).
However BIOS update is for CHIPSET and will not impact for the operating System.
We recommend you to update to the available latest BIOS for unit for better performance:
ROM Firmware for HP Compaq dc7800 (786F1) (International)  | v01.35 Rev.A 27 Nov 2015 |
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Thank You,
GBL84
I am not an HP Employee