Difference between revisions of "Quadratic equation"
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== See Also == | == See Also == | ||
* [[Discriminant]] | * [[Discriminant]] | ||
| + | * [[Vieta's Formulas]] | ||
* [[Quadratic Inequality]] | * [[Quadratic Inequality]] | ||
[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Algebra]] | [[Category:Algebra]] | ||
Revision as of 19:55, 20 June 2011
A quadratic equation in one variable is an equation of the form 
, where 
, 
and 
are constants (that is, they do not depend on 
) and is the unknown variable. Quadratic equations are solved using one of three 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 . Note: This is different for all quadratics; we cleverly chose this so that it has common factors.
Solution:
First, we expand the middle term: 
.
Next, we factor out our common terms to get 
.
We can now factor the 
term to get 
. By the zero-product property, either or 
equals zero.
We now have the pair of equations 
and 
. These give us the answers 
and 
, which can also be written as 
. 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.
