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IberoAmerican
1990 IberoAmerican
6
6
Part of
1990 IberoAmerican
Problems
(1)
About the graph of a polynomial
Source: Iberoamerican Olympiad 1990, Problem 6
5/18/2007
Let
f
(
x
)
f(x)
f
(
x
)
be a cubic polynomial with rational coefficients. If the graph of
f
(
x
)
f(x)
f
(
x
)
is tangent to the
x
x
x
axis, prove that the roots of
f
(
x
)
f(x)
f
(
x
)
are all rational.
algebra
polynomial
algebra proposed