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1976 IMO Shortlist
8
8
Part of
1976 IMO Shortlist
Problems
(1)
Prove that there exist polynomials P and Q
Source:
9/20/2010
Let
P
P
P
be a polynomial with real coefficients such that
P
(
x
)
>
0
P(x) > 0
P
(
x
)
>
0
if
x
>
0
x > 0
x
>
0
. Prove that there exist polynomials
Q
Q
Q
and
R
R
R
with nonnegative coefficients such that
P
(
x
)
=
Q
(
x
)
R
(
x
)
P(x) = \frac{Q(x)}{R(x)}
P
(
x
)
=
R
(
x
)
Q
(
x
)
if
x
>
0.
x > 0.
x
>
0.
algebra
polynomial
coefficients
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