Should I just solve all my quadratic equations by using the quadratic formula since it always works?

Question

I know there are 3 ways to solving quadratic equations: factoring, square roots, and quad. form. But is it easier to just solve all my quad. equations by using the quadratic formula? Do I HAVE to know the other 2 methods?

Answer 1

No, factoring (where feasible) is faster.  If not obvious how to factor, calculate the discriminant (b²-4ac).

 

If discriminant < 0, there are only complex roots. If discriminant = 0, there's only a so-called 'double' root (one real number of MULTIPLICITY TWO). 

 

If discriminant equals a perfect square, then you could have factored because there are two Real roots.

 

If discriminant > 0 but is not a perfect square, there's a conjugate pair of irrational roots.