Difference between revisions of "Perfect square"

Revision as of 11:02, 29 June 2006

An integer $n$ is said to be a perfect square if there is an integer $m$ so that $m^2=n$ . The first few perfect squares are 0, 1, 4, 9, 16, 25, 36.

The sum of the first $n$ square numbers (not including 0) is $\frac{n(n+1)(2n+1)}{6}$

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Perfect Square Trinomials

Another type of perfect square is an equation that is a perfect square trinomial. Take for example

$(x+a)^2=x^2+2xa+a^2$ .

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 $ax^2+bx+c$ , it is a perfect square trinomial iff $b=a\sqrt{c}$ .

@@ Line 4: / Line 4: @@
 {{stub}}
+== Perfect Square Trinomials ==
+Another type of perfect square is an equation that is a perfect square trinomial.  Take for example
+<math>(x+a)^2=x^2+2xa+a^2</math>.
+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 <math>ax^2+bx+c</math>, it is a perfect square trinomial [[iff]] <math>b=a\sqrt{c}</math>.

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Difference between revisions of "Perfect square"

Revision as of 11:02, 29 June 2006

Perfect Square Trinomials