Difference between revisions of "Perfect square"
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For any quadratic equation in the form <math>ax^2+bx+c</math>, it is a perfect square trinomial [[iff]] <math>b=a\sqrt{c}</math>. | For any quadratic equation in the form <math>ax^2+bx+c</math>, it is a perfect square trinomial [[iff]] <math>b=a\sqrt{c}</math>. | ||
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==See also == | ==See also == | ||
* [[Perfect cube]] | * [[Perfect cube]] | ||
* [[Perfect power]] | * [[Perfect power]] | ||
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{{stub}} | {{stub}} | ||
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| + | [[Category:Definition]] | ||
Revision as of 14:34, 19 April 2008
An integer 
is said to be a perfect square if there is an integer 
so that 
. The first few perfect squares are 0, 1, 4, 9, 16, 25, 36.
The sum of the first square numbers (not including 0) is 
An integer is a perfect square iff it is a quadratic residue modulo all but finitely primes.
Perfect Square Trinomials
Another type of perfect square is an equation that is a perfect square trinomial. Take for example
.
Perfect square trinomials are a type of quadratic equation that have 3 terms and contain 1 unique root.
For any quadratic equation in the form 
, it is a perfect square trinomial iff 
.
See also
This article is a stub. Help us out by expanding it.
