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Source:
January 9, 2022
algebra
Problem Statement
The polynomial
f
(
x
)
=
x
3
+
r
x
2
+
s
x
+
t
f(x) = x^3 + rx^2 + sx + t
f
(
x
)
=
x
3
+
r
x
2
+
s
x
+
t
has
r
,
s
r, s
r
,
s
, and
t
t
t
as its roots (with multiplicity), where
f
(
1
)
f(1)
f
(
1
)
is rational and
t
≠
0
t \ne 0
t
=
0
. Compute
∣
f
(
0
)
∣
|f(0)|
∣
f
(
0
)
∣
.
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