Question 420491
The quadratic formula guarantees the solutions, even though it might require more arithmetic than factoring. Also, it works when the solutions are complex. Completing the square is also guaranteed to work, unless the coefficients become crazy. Factoring, in reality, assumes you know the zeros. However factoring a quadratic is easiest when the roots are integers, and it is much harder when the polynomial is not monic (i.e. the x^2 coefficient is not 1). It's hard to judge which method is most appropriate, because each method has its pros and cons.