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Byju's Answer
Standard XII
Mathematics
Descartes' Rule
Let fx be a p...
Question
Let
f
(
x
)
be a polynomial of degree
3
such that
f
(
k
)
=
−
2
k
for
k
=
2
,
3
,
4
,
5
. Then the value of
52
−
10
f
(
10
)
is equal to
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Solution
Let
P
(
k
)
=
k
f
(
k
)
+
2
⇒
k
f
(
k
)
+
2
=
a
(
x
−
2
)
(
x
−
3
)
(
x
−
4
)
(
x
−
5
)
If
k
=
0
⇒
2
=
a
(
−
2
)
(
−
3
)
(
−
4
)
(
−
5
)
∴
a
=
1
60
⇒
k
f
(
k
)
+
2
=
1
60
(
x
−
2
)
(
x
−
3
)
(
x
−
4
)
(
x
−
5
)
Putting
k
=
10
⇒
10
f
(
10
)
+
2
=
1
60
⋅
8
⋅
7
⋅
6
⋅
5
=
28
∴
10
f
(
10
)
=
26
⇒
52
−
10
f
(
10
)
=
26
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