I’m trying to re-purpose a subwoofer, which I originally bought for a home theater system. What I would like to do is introduce it into my bedroom studio set up. My audio interface is a Focusrite Scarlett 2i4, which has a balanced L/R pair of ¼” outs and an unbalanced pair of RCA outs.
 
Right now, the balanced ¼” Scarlett “outs” are running directly into balanced “ins” on a pair of Rokit 6 monitors. Before now, back when I first set up, I had a really irritating low-level hum in the monitors. Turns out, I was getting the noise because I was using unbalanced ¼” cables from the Scarlett to the monitors. Doh! I switched to balanced cables and the monitor hum went away. Life was good.
 
The only connections on the subwoofer, a Velodyne DLS-3750R, are RCAs (L/R), a pair for input and a pair for output (plus speaker-level outs, but that doesn’t seem to matter here). My limited understanding is that there’s no such thing as a balanced RCA connection or cable, so I’m assuming that these subwoofer connections are unbalanced.
 
I’m not an electronics whiz, so I would just like to confirm what I believe to be true; that is: I’m likely to re-introduce noise into my signal flow if I introduce unbalanced RCA cables into my set-up – from the Scarlett “out” to the subwoof “in”, and from the subwoof “out” to the monitors “in” – even if I try using RCA-to-1/4” balanced adapters.
 
Am I assuming correctly? Is this old home theater subwoofer just not a good fit? Thanks for any insight!

Okay, I haven't downloaded the manual but it seems the Velodyne DLS-3750R is a 10" woofer with a built-in amplifier and a DSP with four listening modes.
 
The DSP listening modes do not have a flat listening mode, the DSP is going to apply EQ and color the sound.  That's bad when you're mixing tracks.
 
If you decide it's worth a try, you want the computer stereo output to go to the Velodyne inputs.  You want the Rokit 6 speakers to plug into the Velodyne.  Then you'll use the low pass crossover to blend the sound of the Velodyne and Rokit speakers.

Just hook up the RCA in/outs and see what happens.
I have a Yamaha home Sub that has RCA inputs and I use the RCA outs from the small mixer I use for monitoring. 
I don't hear any hum. I'm using real good quality, gold plated, heavy copper shielding, RCA cables. 
Just aviod cheap RCA cables with molded ends. Gets some good one. I get mine from the Goodwill store. 
 

You are correct insofar as going to RCA connectors will defeat all or some of the benefits of balanced cables. It's quite likely that your sub's post-crossover outputs are unbalanced as well.
 
Give it a go and see if the hum comes back. It might not. If it does, then you may have no choice but to use a separate crossover rather than the one built in to the subwoofer. That, unfortunately, raises its own challenges because most active crossovers accept only balanced XLR inputs and outputs. You'd have to find or make an XLR-to-RCA adapter.
 

<<The DSP listening modes do not have a flat listening mode, the DSP is going to apply EQ and color the sound.  That's bad when you're mixing tracks.>>
 
Good point. Never thought about the frequency response options available in the sub. So, I guess if you get a sub like those from, say, KRK (I have their Rokit 6 near-field monitors), those are dialed in, in terms of freq. response.
 
And, yeah, I guess try it. What's the worst that can happen? It hums and I move on! Thanks all. 

Well. No-go. Adding subwoofer into the signal chain introduced terrible noise/hum in the monitors. With only unbalanced ins and outs on the sub, what can you say? It is what it is.   

First thing to look at is your RCA cable. Use the best cable you can afford. Since it uses RCA connectors, it won't be balanced nor have any of the benefits of balanced connections. But high quality cable will be quieter and reject noise better than your typical radio shack cheapo wires. 
 
Next I'd connect both the sub and your monitors to your interface directly. Use the RCA connections to go to the sub and the balanced connections/cable to go to your monitors. Then try ground lifting your sub and see what you get.
 
Yes you will still be feeding low frequencies to your monitors but it shouldn't matter too much. If you really want to get over the top about it, you could keep an eye on craigslist for a 2nd hand crossover and run balanced connections from your interface to that to your monitors. 

JohanSebatianGremlin
First thing to look at is your RCA cable. Use the best cable you can afford. Since it uses RCA connectors, it won't be balanced nor have any of the benefits of balanced connections. But high quality cable will be quieter and reject noise better than your typical radio shack cheapo wires. 
 
Next I'd connect both the sub and your monitors to your interface directly. Use the RCA connections to go to the sub and the balanced connections/cable to go to your monitors. Then try ground lifting your sub and see what you get.
 
Yes you will still be feeding low frequencies to your monitors but it shouldn't matter too much. If you really want to get over the top about it, you could keep an eye on craigslist for a 2nd hand crossover and run balanced connections from your interface to that to your monitors. 

Yeah, the RCA cables are ridiculously priced Monster cables, gold connections, triple-wound blah blah blah, the whole 9 yards. Still sounds terrible. I wondered about coming out of the unbalanced RCA connections available on the interface and going directly to the sub, while keeping the balanced quarter inch outs going to the monitors.

JohanSebatianGremlin
First thing to look at is your RCA cable. Use the best cable you can afford. Since it uses RCA connectors, it won't be balanced nor have any of the benefits of balanced connections. But high quality cable will be quieter and reject noise better than your typical radio shack cheapo wires. 
 
Next I'd connect both the sub and your monitors to your interface directly. Use the RCA connections to go to the sub and the balanced connections/cable to go to your monitors. Then try ground lifting your sub and see what you get.
 
Yes you will still be feeding low frequencies to your monitors but it shouldn't matter too much. If you really want to get over the top about it, you could keep an eye on craigslist for a 2nd hand crossover and run balanced connections from your interface to that to your monitors. 

So it worked going out of my 2i4 direct to the sub, but like you say, no crossover in the signal flow. Will check into an external crossover, and try to wrestle this down yet. Funny thing, I couldn't get any signal out of the interface's  channels 3&4 RCA outs, but I can out of the 1&2 RCA outs, which the manual says carries the same signal as the 1&2 balanced 1/4" outs. Makes me curious what 3&4 are carrying then, if not the same signal as channels 1&2??

There is another thing you might check regarding the hum issue. Balanced connections can be an improvement on long runs, say more than 25 feet, but if you're getting a lot of hum from short unbalanced connections, there might be another cause. If the grounding of the electrical circuits in your home is not consistent from one circuit to another, and your audio equipment is plugged into multiple circuits, that can definitely cause a significant hum. If that is the cause, plugging all connected audio equipment into the same circuit may alleviate some or all of the hum.