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Regional Mathematical Olympiad
2015 India Regional MathematicaI Olympiad
2
RMO Delhi Q.2
RMO Delhi Q.2
Source:
December 20, 2015
RMO 2015
Problem Statement
2.Let
P
(
x
)
=
x
2
+
a
x
+
b
P(x) = x^2 + ax + b
P
(
x
)
=
x
2
+
a
x
+
b
be a quadratic polynomial where a, b are real numbers. Suppose
P
(
ā
1
)
2
P(-1)^2
P
(
ā
1
)
2
,
P
(
0
)
2
P(0)^2
P
(
0
)
2
,
P
(
1
)
2
P(1)^2
P
(
1
)
2
is an Arithmetic progression of positive integers. Prove that a, b are integers.
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