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Purple Comet Problems
2017 Purple Comet Problems
15
Purple Comet 2017 HS problem 15
Purple Comet 2017 HS problem 15
Source:
March 19, 2020
polynomial
algebra
Problem Statement
For real numbers
a
,
b
a, b
a
,
b
, and
c
c
c
the polynomial
p
(
x
)
=
3
x
7
−
291
x
6
+
a
x
5
+
b
x
4
+
c
x
2
+
134
x
−
2
p(x) = 3x^7 - 291x^6 + ax^5 + bx^4 + cx^2 + 134x - 2
p
(
x
)
=
3
x
7
−
291
x
6
+
a
x
5
+
b
x
4
+
c
x
2
+
134
x
−
2
has
7
7
7
real roots whose sum is
97
97
97
. Find the sum of the reciprocals of those
7
7
7
roots.
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