Quadratic equation: Difference between revisions
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= | A '''quadratic equation''' is an [[equation]] of form <math> {a}{x}^2+{b}{x}+{c}=0</math>. a, b, and c are [[constant]]s, and x is the unknown [[variable]]. Quadratic equations are solved using 3 main strategies: [[factoring]], [[completing the square]], and the [[quadratic formula]]. | ||
=== Factoring === | === Factoring === | ||
The purpose of factoring is to turn a general quadratic into a product of | The purpose of factoring is to turn a general quadratic into a product of [[binomial]]s. This is easier to illustrate than to describe. | ||
Example: Solve the equation <math>x^2-3x+2=0</math> for x. | Example: Solve the equation <math>x^2-3x+2=0</math> for x. | ||
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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. | 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 === | === Completing the square === | ||
Revision as of 19:44, 23 July 2006
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.
