Question

Which method(s) do(es) not work every time when solving quadratic equations?

Select all that apply

the quadratic formula

factoring

taking roots

completing the square

Answer 1

Factoring and taking roots do not work every time.

- Factoring: Many quadratics don’t factor nicely (over the integers or rationals), e.g. x^2 + x + 1.
- Taking roots (square-root method): Only works when you can rewrite the equation as (expression)^2 = constant (no linear term), otherwise it doesn’t apply.

Completing the square and the quadratic formula always work (they produce the roots, real or complex).