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4
2009 Calculus #4: Fourth Degree Polynomial
2009 Calculus #4: Fourth Degree Polynomial
Source:
June 23, 2012
calculus
algebra
polynomial
derivative
Problem Statement
Let
P
P
P
be a fourth degree polynomial, with derivative
P
′
P^\prime
P
′
, such that
P
(
1
)
=
P
(
3
)
=
P
(
5
)
=
P
′
(
7
)
=
0
P(1)=P(3)=P(5)=P^\prime (7)=0
P
(
1
)
=
P
(
3
)
=
P
(
5
)
=
P
′
(
7
)
=
0
. Find the real number
x
≠
1
,
3
,
5
x\neq 1,3,5
x
=
1
,
3
,
5
such that
P
(
x
)
=
0
P(x)=0
P
(
x
)
=
0
.
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