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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2019 India PRMO
2
Minimal Polynomial
Minimal Polynomial
Source: PRMO 2019 Leg 2 P2
August 25, 2019
algebra
PRMO
polynomial
Problem Statement
If
x
=
2
+
3
+
6
x=\sqrt2+\sqrt3+\sqrt6
x
=
2
+
3
+
6
is a root of
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
=
0
x^4+ax^3+bx^2+cx+d=0
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
=
0
where
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are integers, what is the value of
∣
a
+
b
+
c
+
d
∣
|a+b+c+d|
∣
a
+
b
+
c
+
d
∣
?
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