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2011 VTRMC
Problem 7
Problem 7
Part of
2011 VTRMC
Problems
(1)
P has nonreal root: x^100+20x^99+198x^98+...+1
Source: VTRMC 2011 P7
5/14/2021
Let
P
(
x
)
=
x
100
+
20
x
99
+
198
x
98
+
a
97
x
97
+
…
+
a
1
x
+
1
P(x)=x^{100}+20x^{99}+198x^{98}+a_{97}x^{97}+\ldots+a_1x+1
P
(
x
)
=
x
100
+
20
x
99
+
198
x
98
+
a
97
x
97
+
…
+
a
1
x
+
1
be a polynomial where the
a
i
(
1
≤
i
≤
97
)
a_i~(1\le i\le97)
a
i
(
1
≤
i
≤
97
)
are real numbers. Prove that the equation
P
(
x
)
=
0
P(x)=0
P
(
x
)
=
0
has at least one nonreal root.
algebra
polynomial
Polynomials
roots