411 REFERENCE · Wikibooks
Timeless Theorems of Mathematics/Rational Root Theorem
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
The rational root theorem states that, if a rational number (where and are relatively prime) is a root of a polynomial with integer coefficients, then is a factor of the constant term and is a factor of the leading coefficient. In other words, for the polynomial, , if , (where and ) then and
Proof
Let , where .
Assume for coprime . Therefore,
Let
Thus,
As is coprime to and , thus .
Again,
Let
Thus,
As is coprime to and , thus .
For , if , (where and ) then and . [Proved]
100%