Purple Math
Purplemath: Finding Quadratics From Their Zeroes
Students often have difficulty "working backwards" from the solution of a problem to its original question. Finding a polynomial, given its roots, is an example of a "working backwards" problem. Here are several examples using different...
Wolfram Research
Wolfram Math World: Descartes' Sign Rule
This page gives a good overview of Descartes' Sign Rule, a "method of determining the maximum number of positive and negative real roots of a polynomial."