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very odd failure of Solve


Setting an irrelevant parameter to 0 baffles Solve. Why?
Thanks,
Alan Isaac

$Assumptions =.
ClearAll[f1]
f1[x_] := s*x^\[Alpha] - (a + b + c)*x
Solve[f1[x] == 0, x]  (* Solve works *)
Solve[(f1[x] /. {b -> 0}) == 0, x]  (* Solve fails *)

(* adding these assumptions does not change things *)
f1assume =  (1 > s > 0 && k >= 0 && 1 > \[Alpha] > 0 && a >= 0 && b >= 0 && 
   1 > c > 0);
Assuming[f1assume, Solve[f1[x] == 0, x]]  (* Solve works *)
Assuming[f1assume,  Solve[(f1[x] /. {b -> 0}) == 0, x]] (* Solve fails *)



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