derivation of quadratic formula
Suppose are real numbers, with , and suppose
Since is nonzero, we can divide by and obtain the equation
where and . This equation can be written as
so completing the square, i.e., applying the identity , yields
Then, taking the square root of both sides, and solving for , we obtain the solution formula
and the derivation is completed.
A slightly less intuitive but more aesthetically pleasing approach to this derivation can be achieved by multiplying both sides of the equation
by , resulting in the equation
in which the left-hand side can be expressed as . From here, the proof is identical.
|Title||derivation of quadratic formula|
|Date of creation||2013-03-22 11:56:44|
|Last modified on||2013-03-22 11:56:44|
|Last modified by||mathcam (2727)|