Using a range extender with AC1750 WiFi DOCSIS 3.0 Cable Modem Router

Your range extender will extend only 2.4 GHz Wi-Fi.  It will not be able to assist any devices that use 5 GHz.  Those devices will either need to connect directly to your new modem/router, or you will need to constrain them to 2.4 GHz, or you can buy a dual-band extender.  But read on before deciding.

Consider this.  While 5 GHz signals degrade much faster than 2.4 GHz as distances increases, it is often able to maintain much higher speeds due to wider channels (typically 40 MHz and 80 MHz vs 20 MHz that typically achievable at 2.4 GHz) and superior protocols (i.e. 802.11ac, though your devices must also support it).  Your 5 GHz-capable devices may do just fine without the assistance of a range extender.  Your results will depend very much on the layout, size and construction materials of your residence.  

Try out your new modem/router.  If well placed, it may be powerful enough on its own to reach most parts of your place.  Then you can tactically place your extender to provide coverage to one or more dead spots.  If you give both the 2.4 GHz and 5 GHz networks the same name, then your dual-band devices can dynamically pick the best frequency to operate at.