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Indonesia MO
2020 Indonesia MO
2
2
Part of
2020 Indonesia MO
Problems
(1)
System of Quadratic Polynomials: sum equal to zero or not all are distinct
Source: Indonesian MO (INAMO) 2020, Day 1, Problem 2
10/13/2020
Problem 2. Let
P
(
x
)
=
a
x
2
+
b
x
+
c
P(x) = ax^2 + bx + c
P
(
x
)
=
a
x
2
+
b
x
+
c
where
a
,
b
,
c
a, b, c
a
,
b
,
c
are real numbers. If
P
(
a
)
=
b
c
,
P
(
b
)
=
a
c
,
P
(
c
)
=
a
b
P(a) = bc, \hspace{0.5cm} P(b) = ac, \hspace{0.5cm} P(c) = ab
P
(
a
)
=
b
c
,
P
(
b
)
=
a
c
,
P
(
c
)
=
ab
then prove that
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
(
a
+
b
+
c
)
=
0.
(a - b)(b - c)(c - a)(a + b + c) = 0.
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
(
a
+
b
+
c
)
=
0.
quadratics
algebra
polynomial
2020
Indonesia MO
Indonesian MO