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Thailand TST Selection Test
2022 Thailand TSTST
1
Polynomial equation
Polynomial equation
Source: Thailand TSTST 2021, test 3, P1
August 16, 2022
algebra
Problem Statement
Find all polynomials
f
,
g
,
h
f, g, h
f
,
g
,
h
with real coefficients, such that
f
(
x
)
2
+
(
x
+
1
)
g
(
x
)
2
=
(
x
3
+
x
)
h
(
x
)
2
f(x)^2+(x+1)g(x)^2=(x^3+x)h(x)^2
f
(
x
)
2
+
(
x
+
1
)
g
(
x
)
2
=
(
x
3
+
x
)
h
(
x
)
2
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