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National and Regional Contests
Turkey Contests
National Olympiad First Round
2001 National Olympiad First Round
4
4
Part of
2001 National Olympiad First Round
Problems
(1)
P04 [Algebra] - Turkish NMO 1st Round - 2001
Source:
4/18/2014
How many real solution does the equation
x
2000
2001
+
2
3
x
2
−
2
5
x
+
3
\dfrac{x^{2000}}{2001} + 2\sqrt 3 x^2 - 2\sqrt 5 x + \sqrt 3
2001
x
2000
+
2
3
x
2
−
2
5
x
+
3
have?
<
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(
A
)
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0
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(
B
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1
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(
C
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11
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(
D
)
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12
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(
E
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None of the preceding
<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 11 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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(
A
)
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0
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(
B
)
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1
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(
C
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11
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−
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>
(
D
)
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12
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−
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>
(
E
)
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None of the preceding
algebra
polynomial