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### Names of Polynomials

```
Date: 05/22/99 at 15:59:52
From: Rohan
Subject: Why is an equation having only two roots, one of which is
raised to 2, called a "quadratic equation"?

QUAD means four. But why is an equation having ONLY TWO ROOTS, one of
which is raised to 2, called a "QUADRATIC EQUATION"?

For example: - ax^2 + bx + c
```

```
Date: 05/22/99 at 20:40:32
From: Doctor Peterson
Subject: Re: Why is an equation having only two roots, one of which is
raised to 2, called a "quadratic equation"?

Hi, Rohan.

second power, not the fourth. But there's another dimension to the
word.

means a square (because it has four sides) and "quadratus" means
"squared." We get several other words from this: "quadrille," meaning
a square dance; "quadrature," meaning constructing a square of a
certain area; and even "square" (through French).

Quadratic equations originally came up in connection with geometric
problems involving squares, and of course the second power is also
called a "square," which accounts for the name. The third-degree
equation is similarly called a "cubic," based on the shape of a third
power. Then when higher-degree equations began to be studied, the
names for them were formed differently, based on degree rather than
shape (since the Romans had no words for higher-dimensional shapes),
giving us the quartic, quintic, and so on. In fact, quartic came
along later; originally a fourth degree equation was called
"biquadratic," meaning "doubly squared," which mixes the two concepts
and is doubly confusing.

So here's a table of names for polynomials and their sources:

degree   name        shape    dimension
------   ---------   ------   ---------
1     linear      line        (1)
3     cubic       cube        (3)
4     quartic      -           4
5     quintic      -           5

You may be interested in a discussion of this question in the archives
of the math-history discussion group:

http://mathforum.org/kb/message.jspa?messageID=1376346

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
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