Section 56: Problem 2 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Find a circle about the origin containing all the roots of the polynomial equation
.
If
, then for
,
has all roots inside
if
, i.e.
. If
, then it holds. Now,
iff
, so that all roots of
are inside
for any
, in particular, for
.