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USAMO 1983 Problem 2 - Roots of Quintic
USAMO 1983 Problem 2 - Roots of Quintic
Source: USAMO 1983 Problem 2
August 16, 2011
USA(J)MO
USAMO
calculus
derivative
quadratics
algebra
Hi
Problem Statement
Prove that the roots of
x
5
+
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
x^5 + ax^4 + bx^3 + cx^2 + dx + e = 0
x
5
+
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
cannot all be real if
2
a
2
<
5
b
2a^2 < 5b
2
a
2
<
5
b
.
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