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2011 AIME Problems
15
Cubic, Integer Solutions
Cubic, Integer Solutions
Source:
March 18, 2011
algebra
polynomial
Vieta
quadratics
AMC
AIME
YUH.
Problem Statement
For some integer
m
m
m
, the polynomial
x
3
−
2011
x
+
m
x^3-2011x+m
x
3
−
2011
x
+
m
has the three integer roots
a
a
a
,
b
b
b
, and
c
c
c
. Find
∣
a
∣
+
∣
b
∣
+
∣
c
∣
|a|+|b|+|c|
∣
a
∣
+
∣
b
∣
+
∣
c
∣
.
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