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National Olympiad First Round
2000 National Olympiad First Round
16
Turkey NMO 2000 1st Round - P16 (Algebra)
Turkey NMO 2000 1st Round - P16 (Algebra)
Source:
July 25, 2012
algebra
polynomial
function
Problem Statement
What is the sum of real roots of
(
2
+
(
2
+
(
2
+
x
)
2
)
2
)
2
=
2000
(2+(2+(2+x)^2)^2)^2=2000
(
2
+
(
2
+
(
2
+
x
)
2
)
2
)
2
=
2000
?
<
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n
c
l
a
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a
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x
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b
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′
>
(
A
)
<
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p
a
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>
−
4
<
s
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c
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a
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s
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x
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>
(
B
)
<
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−
2
<
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−
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>
(
C
)
<
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a
n
>
0
<
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c
l
a
s
s
=
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a
t
e
x
−
b
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′
>
(
D
)
<
/
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a
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>
2
<
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c
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a
s
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=
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>
(
E
)
<
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>
4
<span class='latex-bold'>(A)</span>\ -4 \qquad<span class='latex-bold'>(B)</span>\ -2 \qquad<span class='latex-bold'>(C)</span>\ 0 \qquad<span class='latex-bold'>(D)</span>\ 2 \qquad<span class='latex-bold'>(E)</span>\ 4
<
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p
an
c
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a
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−
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′
>
(
A
)
<
/
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p
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>
−
4
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s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
−
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
4
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