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Purple Comet Problems
2016 Purple Comet Problems
17
Purple Comet 2016 HS Problem 17
Purple Comet 2016 HS Problem 17
Source:
April 12, 2018
Purple Comet
Problem Statement
The cubic polynomials
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
satisfy •
p
(
1
)
=
q
(
2
)
p(1) = q(2)
p
(
1
)
=
q
(
2
)
•
p
(
3
)
=
q
(
4
)
p(3) = q(4)
p
(
3
)
=
q
(
4
)
•
p
(
5
)
=
q
(
6
)
p(5) = q(6)
p
(
5
)
=
q
(
6
)
•
p
(
7
)
=
q
(
8
)
+
13
p(7) = q(8) + 13
p
(
7
)
=
q
(
8
)
+
13
. Find
p
(
9
)
−
q
(
10
)
p(9)-q(10)
p
(
9
)
−
q
(
10
)
.
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