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CIIM
2018 CIIM
Problem 4
Problem 4
Part of
2018 CIIM
Problems
(1)
CIIM 2018 Problem 4
Source:
3/10/2019
Let
α
<
0
<
β
\alpha < 0 < \beta
α
<
0
<
β
and consider the polynomial
f
(
x
)
=
x
(
x
−
α
)
(
x
−
β
)
f(x) = x(x-\alpha)(x-\beta)
f
(
x
)
=
x
(
x
−
α
)
(
x
−
β
)
. Let
S
S
S
be the set of real numbers
s
s
s
such that
f
(
x
)
−
s
f(x) - s
f
(
x
)
−
s
has three different real roots. For
s
∈
S
s\in S
s
∈
S
, let
p
(
x
)
p(x)
p
(
x
)
the product of the smallest and largest root of
f
(
x
)
−
s
f(x)-s
f
(
x
)
−
s
. Determine the smallest possible value that
p
(
s
)
p(s)
p
(
s
)
for
s
∈
S
s\in S
s
∈
S
.
CIIM2018
undergraduate