kill(all)$

van=facebook.com/LearningCalculus$

      Problem: Prove that f(x) has exactly two solutions:

f(x):=x^4+5*x^3+6*x^2-4*x-16$

s:solve(f(x),x);

      Since f(x) is a quartic polynomial we expect four solutions.
      We find four solutions,two are real, two are complex, no multiple roots.
      To confirm our solution is complete (the proof) we back substitute:

(f(rhs(s[1])));

for i: 1 thru 4 do
print("Answer Proof:", rhs(s[i]), " solves ", (f(rhs(s[i]))), " = ",
       (fullratsimp(f(rhs(s[i])))))$