Different Ways of Solving the Quadratic, via Square Roots

Stub explanation

In introduction to the quadratic formula, we saw that a quadratic $ax^2 + bx + c$ (with nonzero leading coefficient $a\ne0$) has two (possibly equal) roots, found by completing the square.

Using the method of undetermined coefficients, we can also derive the formula using the factored form of quadratics: $ax^2+bx+c = a(x-r)(x-s)$, where $r,s$ are the roots (possibly equal).