MathDB
Problems
Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
2015 India Regional MathematicaI Olympiad
2
Question 2
Question 2
Source:
December 6, 2015
quadratics
algebra
polynomial
RMO 2015
Problem Statement
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 with real coefficients. Suppose there are real numbers
s
≠
t
s \neq t
s
=
t
such that
P
(
s
)
=
t
P(s) = t
P
(
s
)
=
t
and
P
(
t
)
=
s
P(t) = s
P
(
t
)
=
s
. Prove that
b
−
s
t
b-st
b
−
s
t
is a root of
x
2
+
a
x
+
b
−
s
t
x^2 + ax + b - st
x
2
+
a
x
+
b
−
s
t
.
Back to Problems
View on AoPS