MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2019 Moldova Team Selection Test
9
9
Part of
2019 Moldova Team Selection Test
Problems
(1)
incredible polynomial, 10/10
Source: Moldova TST 2019
3/10/2019
Find all polynomials
P
(
X
)
P(X)
P
(
X
)
with real coefficients such that if real numbers
x
,
y
x,y
x
,
y
and
z
z
z
satisfy
x
+
y
+
z
=
0
,
x+y+z=0,
x
+
y
+
z
=
0
,
then the points
(
x
,
P
(
x
)
)
,
(
y
,
P
(
y
)
)
,
(
z
,
P
(
z
)
)
\left(x,P(x)\right), \left(y,P(y)\right), \left(z,P(z)\right)
(
x
,
P
(
x
)
)
,
(
y
,
P
(
y
)
)
,
(
z
,
P
(
z
)
)
are all colinear.
polynomial
algebra