Difference between revisions of "Quadratic equation"
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A '''quadratic equation''' is an [[equation]] of the form <math> {a}{x}^2+{b}{x}+{c}=0</math>, where <math>a</math>, <math>b</math> and <math>c</math> are [[constant]]s and <math>x</math> is the unknown [[variable]]. Quadratic equations are solved using 3 main strategies: [[factoring]], [[completing the square]] and the [[quadratic formula]]. | A '''quadratic equation''' is an [[equation]] of the form <math> {a}{x}^2+{b}{x}+{c}=0</math>, where <math>a</math>, <math>b</math> and <math>c</math> are [[constant]]s and <math>x</math> is the unknown [[variable]]. Quadratic equations are solved using 3 main strategies: [[factoring]], [[completing the square]] and the [[quadratic formula]]. | ||
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=== Factoring === | === Factoring === | ||
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The purpose of factoring is to turn a general quadratic into a product of [[binomial]]s. This is easier to illustrate than to describe. | The purpose of factoring is to turn a general quadratic into a product of [[binomial]]s. This is easier to illustrate than to describe. | ||
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* [[Discriminant]] | * [[Discriminant]] | ||
* [[Quadratic Inequality]] | * [[Quadratic Inequality]] | ||
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| + | [[Category:Definition]] | ||
Revision as of 21:12, 21 April 2008
A quadratic equation is an equation of the form 
, where 
, 
and 
are constants and 
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 . 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.
