Difference between revisions of "Rational Root Theorem"
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The gives us a relatively quick process to find all "nice" roots of a given polynomial, since given the coefficients we have only a finite number of rational numbers to check. | The gives us a relatively quick process to find all "nice" roots of a given polynomial, since given the coefficients we have only a finite number of rational numbers to check. | ||
| − | + | ==Problems== | |
| + | |||
| + | ===Intermediate=== | ||
| + | |||
| + | Find all rational roots of the polynomial <math>x^4-x^3-x^2+x+57</math> | ||
Revision as of 12:04, 23 September 2007
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Given a polynomial 
with integral coefficients, 
. The Rational Root Theorem states that if 
has a rational root 
with 
relatively prime positive integers, 
is a divisor of 
and 
is a divisor of 
.
As a consequence, every rational root of a monic polynomial with integral coefficients must be integral.
The gives us a relatively quick process to find all "nice" roots of a given polynomial, since given the coefficients we have only a finite number of rational numbers to check.
Problems
Intermediate
Find all rational roots of the polynomial 
