1.Proper nounA theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients."The rational root theorem states that if the rational number
p
/
q
{\displaystyle p/q}
is a root of the polynomial equation
a
n
x
n
+
a
n
−
1
x
n
−
1
+
⋯
+
a
0
=
0
{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{0}=0}
, with
a
0
,
…
a
n
∈
Z
{\displaystyle a_{0},\ldots a_{n}\in \mathbb {Z} }
, then
p
|
a
0
{\displaystyle p\vert a_{0}}
and
q
|
a
n
{\displaystyle q\vert a_{n}}
."