Is it possible to make a 3G Android phone support a 4G sim card network, provided it is rooted and has a micro sim slot?

SOLUTION: Hoping you are asking question as you wish to use a 4G network on your 3G phone. I'm telling you easiest way i know, u can buy an LTE portable mobile hotspotand use 4G internet easily. Voice service anyways is still provided by lower generations even in 4G.

 
[brief explanation from what i have learnt about LTE]
Actually mobile equipment (ME) needs to scan signalling channels in order to register to a valid home network (for voice or data communication) which is done by scanning all the bands of frequency that mobile equipment is capable to communicate with (eg 900 Mhz,1800Mhz…). So there can be two cases:
1) 4G band frequency is not supported by mobile equipment
If this is the case no more discussions are needed as the ME is unable to set any 4g band.
2) 4G band frequency is supported but Mobile Equipment has only 3G capability
Eg- ME has 1800 Mhz 3G band (same band airtel provides 4G network)
So now a whole new discussion comes into picture. The ME needs a few signaling protocols to communicate with nearest network identity (base station in gsm, nodeb in umts, enodeb in Lte) this is done via specific interface (like Um in gsm), so heres my conclusion a 3G phone cannot communicate to a 4G network identity as it is unaware of its language so even if 4G is provided on a 3G band, phone cannot use it.

Additionally i will say mobile world is very large and so any view like it is not possible is knocked out (unless the person is bond in the area), given the incredible computing power in our smartphone hell lot of things are possible off way. So i will say it's not that easy but someone might be working on it somewhere. Keep digging until u find something.

Further resource : What is CSFB and SRVCC in LTE?
NOTE: if answer is helpful hit upvote button, it keeps me going.