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2006 Tournament of Towns
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TOT 2006 Spring - Senior A-Level p3 P(x)=x^4+x^3-3x^2+x+2
TOT 2006 Spring - Senior A-Level p3 P(x)=x^4+x^3-3x^2+x+2
Source:
February 25, 2020
polynomial
algebra
Problem Statement
Consider a polynomial
P
(
x
)
=
x
4
+
x
3
ā
3
x
2
+
x
+
2
P(x) = x^4+x^3-3x^2+x+2
P
(
x
)
=
x
4
+
x
3
ā
3
x
2
+
x
+
2
. Prove that at least one of the coefficients of
(
P
(
x
)
)
k
(P(x))^k
(
P
(
x
)
)
k
, (
k
k
k
is any positive integer) is negative. (5)
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