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13
2018-2019 Fall OMO Problem 13
2018-2019 Fall OMO Problem 13
Source:
November 7, 2018
Problem Statement
Compute the largest possible number of distinct real solutions for
x
x
x
to the equation
x
6
+
a
x
5
+
60
x
4
ā
159
x
3
+
240
x
2
+
b
x
+
c
=
0
,
x^6+ax^5+60x^4-159x^3+240x^2+bx+c=0,
x
6
+
a
x
5
+
60
x
4
ā
159
x
3
+
240
x
2
+
b
x
+
c
=
0
,
where
a
a
a
,
b
b
b
, and
c
c
c
are real numbers.Proposed by Tristan Shin
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