Is it possible to have several solutions in this way to t his equation using Pari/ɢᴘ ?

Bonjour,

I’ve the following equation where the aim is to find /alpha/ and /beta/ 
as integers given /w/ and /v/ as integers

alpha == w (v + w beta)

Of course finding several solution for the equation above is possible, 
but then I want /nfroots()/ to return a second set of possible results 
given /c/ and /b/ and where /x/ is an unknow

xx=alpha^2*x^2+(2*alpha*beta-abs(b))*x+(beta^2-c);
nfroots(,xx);

So I need to find several possible valid values of /alpha/ and /beta/ 
such as a different set of roots from /xx/ are found in the last step 
based on different /alpha/ and /beta/. Is it something possible ? If 
yes, how to do it

currently, I’m using this code to find alpha and beta :

beta=-(V\W);

alpha=W*(V+W*beta);

print("alpha=",alpha);

print("beta=",beta);

where W is a perfect square and V an integer.
Cordialement,