Will Roma make it to the playoffs?
Roma currently in not a safe position and they will meet Tottenham, which I think high unlikely they will beat Tottenham.
However, the teams below Roma rank also unlikely to win.
Real Sociedad vs Ajax, Ajax likely to win.
Braga vs Hoffenheim, Hoffenheim looks strong recently.
FC Twente vs Union St.Gilloise, FC Twente might able to get at least one point.
Nice vs Rangers, Nice might win.
There's need 4 teams to kick Roma to not reach top 24 position, but what I listed above, only two teams are possible to win.
There are 4 more games left, so we really do not know who will do it. Roma is 20th and have 5 points, which is why I believe they are not at safe place at the moment, some teams are at safe positions, seems like 10 points could be the barrier to be in top 24, so reaching 5 more points or more in 4 games could be done but Roma is unlikely to win the next game against Tottenham, so that will be zero points, meaning they need to win some games from whatever remains.
The likely result would be that we are going to see Roma end up dropping out of top 24, and if they recover then that's great but the possibility of them not recovering is there too. With Ranieri taking the position, it looks like we should be seeing how they could do better as well, he is a great manager and should be doing fine as well. I believe they acted very quickly to find a replacement, Ranieri didn't take that much time, the moment Juric was out, Ranieri was in, so that saved them some time.