Rational Root Theorem
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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.
This 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 .
Prove that is irrational, using the Rational Root Theorem.