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National and Regional Contests
India Contests
Regional Mathematical Olympiad
2023 India Regional Mathematical Olympiad
3
RMO KV region P-3
RMO KV region P-3
Source:
October 29, 2023
algebra
Polynomials
polynomial
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial with real coefficients of degree 2. Suppose that for some pairwise distinct real numbers ,
a
,
b
,
c
a,b,c
a
,
b
,
c
we have:\\
f
(
a
)
=
b
c
,
f
(
b
)
=
a
c
,
f
(
c
)
=
a
b
f(a)=bc , f(b)=ac, f(c)=ab
f
(
a
)
=
b
c
,
f
(
b
)
=
a
c
,
f
(
c
)
=
ab
Dertermine
f
(
a
+
b
+
c
)
f(a+b+c)
f
(
a
+
b
+
c
)
in terms of
a
,
b
,
c
a,b,c
a
,
b
,
c
.
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