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Moldova Team Selection Test
1999 Moldova Team Selection Test
9
9
Part of
1999 Moldova Team Selection Test
Problems
(1)
Show that $P(X)$ is a first degree polynomial.
Source: Moldova TST 1999
8/7/2023
Let
P
(
X
)
P(X)
P
(
X
)
be a nonconstant polynomial with real coefficients such that for every rational number
q
q{}
q
the equation
P
(
X
)
=
q
P(X)=q
P
(
X
)
=
q
has no irrational solutions. Show that
P
(
X
)
P(X)
P
(
X
)
is a first degree polynomial.
algebra
polynomial