Solve for x:
without using the rational root theorem.
Hint: There is one integer solution.
There is a way to factor this but if you actually want to slog through it using Cardano's Method I'll give you a hero cookie.
Did you not understand topsquark's post? That is NOT Cardano's method so: NO cookie for you!
However, topsquark, Cardano's method solve the "reduced cubic" of the form . Of course, any cubic can be put in that form but did you mean ?
Am I missing something? Soroban's solution is correct and to the best of my knowledge doesn't use Cardano's method?
yeah we can check check the function for monotonicity
f'(x) should not be equal to 0 in (a,b) and f''(x)>=0 or <=0 for all x in (a,b) (for concavity)
at endpoints a,b mod(f(a)/f'(a))<b-a and mod(f(b)/f'(b))<b-a
i think all these conditions are holding for above