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ISI B.Math Entrance Exam
2010 ISI B.Math Entrance Exam
7
7
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2010 ISI B.Math Entrance Exam
Problems
(1)
I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 7
Source: 0
2/6/2012
We are given
a
,
b
,
c
ā
R
a,b,c \in \mathbb{R}
a
,
b
,
c
ā
R
and a polynomial
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
f(x)=x^3+ax^2+bx+c
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
such that all roots (real or complex) of
f
(
x
)
f(x)
f
(
x
)
have same absolute value. Show that
a
=
0
a=0
a
=
0
iff
b
=
0
b=0
b
=
0
.
algebra
polynomial
trigonometry
algebra proposed