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Byju's Answer
Standard IX
Mathematics
Zeroes of a Polynomial
4. Let P(x) b...
Question
4. Let P(x) be a non-zero polynomial with integer coefficients. If P(n) is divisible by n for each positive integer n, what is the value of P(0)? [0]
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Q.
Let
p
(
x
)
be a polynomial such that
p
(
x
)
−
p
′
(
x
)
=
x
n
, where
n
is a positive integer. Then
p
(
0
)
equals.
Q.
Let
P
(
n
)
=
5
n
−
2
n
,
P
(
n
)
is divisible by
3
λ
where
λ
and
n
both are odd positive integers then the least value of
n
and
λ
will be
Q.
Let
p
(
x
)
be a polynomial such that
p
(
x
)
–
p
′
(
x
)
=
x
n
, where
n
is a positive integer. Then
p
(
0
)
equals
Q.
If
n
is a positive integer and
P
(
n
)
=
n
2
(
n
2
−
1
)
, then
P
(
n
)
is always divisi
ble by
Q.
Let
f
(
x
)
be a polynomial with integer coefficients satisfying
f
(
1
)
=
5
and
f
(
2
)
=
7
. The smallest possible positive value of
f
(
12
)
is
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