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2016 Harvard-MIT Mathematics Tournament
7
2016 Team #7
2016 Team #7
Source:
December 30, 2016
Problem Statement
Let
q
(
x
)
=
q
1
(
x
)
=
2
x
2
+
2
x
−
1
q(x) = q^1(x) = 2x^2 + 2x - 1
q
(
x
)
=
q
1
(
x
)
=
2
x
2
+
2
x
−
1
, and let
q
n
(
x
)
=
q
(
q
n
−
1
(
x
)
)
q^n(x) = q(q^{n-1}(x))
q
n
(
x
)
=
q
(
q
n
−
1
(
x
))
for
n
>
1
n > 1
n
>
1
. How many negative real roots does
q
2016
(
x
)
q^{2016}(x)
q
2016
(
x
)
have?
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