@acer 

P, N are positive real; A is real.

@Carl Love 

Thank you. I thought by using 1 as a third argument I was going to obtain first order terms in k.

Anyway, how can I assume properties for the variables?

For instance, I want to assume P, N, A real.

@acer 

About the B variable: yes, it was a typo. Also, I did use your suggestion to calculate all the roots at once, but I had this file displaying this particular problem and posted here so you guys could see what I meant.

Once again, thanks for your help. Much appreciated!

@Carl Love 

I changed the code a bit when because I needed to add another variable.

This time, the code keeps runnning and the program stops answering.

The last part of the code is what I am trying to do.

Again, thanks for your help.

file3.mw

@Carl Love 

I tried to compile, but it's still no working. I got 10 instead of 5, and I couldn't display the plots.

Please, check the file I'll upload in this comment and see what I'm doing wrong.

I want to plot the five roots (w as a function of k) for some given values of B in the same plot. That's what I tried to do in this code.

Thanks for your help.

file2.mw

When I try to extend this code to a 5th degree polynom, the command

H:=[solve(numer(Hgen),w)]:
indets(%,name);
nops(H);

returns me one solution, when it suppose to return five.

How can I fix this? 

file2.mw

Can anybody help me with that?

Thank you!

@Kitonum 

I can see the plots, but I'm still having the same problem when I execute the plot command:

Pk1 := PLOT(`...`)

The behavior looks correct, but how can I make it look like similar to the k=0 case (file0.mw) if I can't change the plot settings?

As I said, I tried to do it (file2 in the comment above), but go the message "Error, invalid input: Im expects 1 argument, but received 3".

@acer

Ok. I tried another way to solve the problem, using both Maple 12 and Maple 18, still having trouble.

I posted the followups here.

I tried another way to fix the problem.

In one file (file1.mw), I solved the equation, selected and converted to string each one of the three solutions.

In another file (file2.mw), I made the solutions functions of (B,V,k), and then tried to plot to V=0.8, V=0.9, V=0.99, k=1, but the message "Error, invalid input: Im expects 1 argument, but received 3" appears. I'm going to do the same for k=5, but first I need to fix this problem.

P.S.: I did it both using Maple 12 and Maple 18, still getting the same problem.

@Kitonum 

Still the same problem, even using Maple 12 or 18.

I tried another way to solve it, but I got another error this time. ("Error, invalid input: Im expects 1 argument, but received 3")

I used one file (file1.mw) to solve the equation, select and convert the three elements to string.

In another worksheet (file2.mw), I defined functions to each element in the previous file, and then tried to plot each function for V=0.8, V=0.9, V=0.99, all for k=1. I'm going to do the same for k=5, but first I need to fix this error.

I appreciate your time and patience.

@acer

I see, good to know.

Is there another way to dimension the plot in Maple 12?

@acer 

If I put a '_' as a overscript, it will work like a 'bar'?

Also, when I use the command 'size=[600,200]' inside the plot command (which is working fine without this command), it gives me the message:

"Error, (in plot) unexpected options: [ArrayTools:-Size = [600, 200] (...)".

mapleprimestest.mw

@acer 

I'm using Maple 12.

In this worksheet, the problem is more evident.

First, I solved for k=0, as you can see. Then, I tried to solve in the general case, for k!=0, but had trouble. I expect the plots to be similar to the k=0 case.

I know it's probably not the smartest way to do this, but is the one I know, but, as I said earlier, I am new to Maple.

@acer 

I'm sorry about that. I thought I provided what was asked. I'm really new to Maple and English is not my mother language, yet I really appreaciate all your help.

Anyway, when I run the code you uploaded, I get the message "Error, (in solve) invalid arguments".

I really thought I made myself clear using the expression "root". Probably a translation issue, my bad. All I want is to plot Im(w) versus B for V=0.8, V=0.9 and V=0.99 for k=1 and k=5.

Again, thank you so much for your time and help.