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ISI Entrance Examination
2020 ISI Entrance Examination
1
1
Part of
2020 ISI Entrance Examination
Problems
(1)
ISI 2020 : Problem 1
Source: B.Stat & B.Math Entrance Exam 2020
9/20/2020
Let
i
i
i
be a root of the equation
x
2
+
1
=
0
x^2+1=0
x
2
+
1
=
0
and let
ω
\omega
ω
be a root of the equation
x
2
+
x
+
1
=
0
x^2+x+1=0
x
2
+
x
+
1
=
0
. Construct a polynomial
f
(
x
)
=
a
0
+
a
1
x
+
⋯
+
a
n
x
n
f(x)=a_0+a_1x+\cdots+a_nx^n
f
(
x
)
=
a
0
+
a
1
x
+
⋯
+
a
n
x
n
where
a
0
,
a
1
,
⋯
,
a
n
a_0,a_1,\cdots,a_n
a
0
,
a
1
,
⋯
,
a
n
are all integers such that
f
(
i
+
ω
)
=
0
f(i+\omega)=0
f
(
i
+
ω
)
=
0
.
isi
2020
polynomial
complex numbers
algebra