Difference between revisions of "Quadratic equation"
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=== Quadratic Formula === | === Quadratic Formula === | ||
See [[Quadratic Formula]]. | See [[Quadratic Formula]]. | ||
| + | |||
| + | == See Also == | ||
| + | * [[Discriminant]] | ||
| + | * [[Quadratic Inequality]] | ||
Revision as of 20:19, 23 July 2006
Quadratic Equations
A quadratic equation is an equation of form 
. a, b, and c are constants, and x is the unknown variable. Quadratic Equations are solved using 3 main strategies: factoring, completing the square, and the quadratic formula.
Factoring
The purpose of factoring is to turn a general quadratic into a product of binomials. This is easier to illustrate than to describe.
Example: Solve the equation 
for x.
Solution:
First we expand the middle term. This is different for all quadratics. We cleverly choose this so that it has common factors. We now have 
.
Next, we factor out our common terms to get: 
.
We can now factor the (x-1) term to get: 
. By a well known theorem, either 
or 
equals zero.
We now have the pair of equations x-1=0, or x-2=0. These give us answers of x=1 or x=2. Plugging these back into the original equation, we find that both of these work! We are done.
Completing the square
Quadratic Formula
See Quadratic Formula.
