Graphic cards must support HDMI 2.0 for higher resolution and refresh rates?

[potatochobit]

even with a high speed HDMI cable, that does 4k @60FPS

 

if the graphic card does not support HDMI 2.0, the refresh rate will be capped at 30FPS?

 

I Have an R9 290X and am wondering how I can run at 1440p via HDMI

or if I need to replace the card 

yes, I am using display port but that is not compatible with anything else