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Hungary Contests
Kürschák Math Competition
1983 Kurschak Competition
2
2
Part of
1983 Kurschak Competition
Problems
(1)
f(2) >= 3^n for polynomial with n real roots and non-negative coefficients
Source: 1983 Hungary - Kürschák Competition p2
10/10/2022
Prove that
f
(
2
)
≥
3
n
f(2) \ge 3^n
f
(
2
)
≥
3
n
where the polynomial
f
(
x
)
=
x
n
+
a
1
x
n
−
1
+
.
.
.
+
a
n
−
1
x
+
1
f(x) = x_n + a_1x_{n-1} + ...+ a_{n-1}x + 1
f
(
x
)
=
x
n
+
a
1
x
n
−
1
+
...
+
a
n
−
1
x
+
1
has non-negative coefficients and
n
n
n
real roots.
algebra
polynomial