Rational Zero Theorem
المؤلف:
Bold, B
المصدر:
Famous Problems of Geometry and How to Solve Them. New York: Dover
الجزء والصفحة:
...
17-2-2019
1114
Rational Zero Theorem
If the coefficients of the polynomial
 |
(1)
|
are specified to be integers, then rational roots must have a numerator which is a factor of 
and a denominatorwhich is a factor of 
(with either sign possible). This follows since a polynomial of polynomial order 
with 
rational roots can be expressed as
 |
(2)
|
where the roots are 
, 
, ..., and 
. Factoring out the 
s,
 |
(3)
|
Now, multiplying through,
 |
(4)
|
where we have not bothered with the other terms. Since the first and last coefficients are 
and 
, all the rational roots of equation (1) are of the form [factors of 
]/[factors of 
].
REFERENCES:
Bold, B. Famous Problems of Geometry and How to Solve Them. New York: Dover, p. 34, 1982.
Niven, I. M. Numbers: Rational and Irrational. New York: Random House, 1961.
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