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Saint Petersburg Mathematical Olympiad
2009 Saint Petersburg Mathematical Olympiad
7
Discriminants
Discriminants
Source: St Petersburg Olympiad 2009, Grade 9, P7
August 30, 2017
algebra
Problem Statement
Discriminants of square trinomials
f
(
x
)
,
g
(
x
)
,
h
(
x
)
,
f
(
x
)
+
g
(
x
)
,
f
(
x
)
+
h
(
x
)
,
g
(
x
)
+
h
(
x
)
f(x),g(x),h(x),f(x)+g(x),f(x)+h(x),g(x)+h(x)
f
(
x
)
,
g
(
x
)
,
h
(
x
)
,
f
(
x
)
+
g
(
x
)
,
f
(
x
)
+
h
(
x
)
,
g
(
x
)
+
h
(
x
)
equals
1
1
1
. Prove that
f
(
x
)
+
h
(
x
)
+
g
(
x
)
≡
0
f(x)+h(x)+g(x) \equiv 0
f
(
x
)
+
h
(
x
)
+
g
(
x
)
≡
0
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