NIMCET 2023 Question Paper with solutions

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Question : 23 of 120

Marks: +1, -0

Let

f(x)

be a polynomial of degree 4 and

f(n)=n+1

for

n=1,2,3,4

. Now, if

f(0)=

25 , then

f(5)

is equal to:

25
None of these
20
30

Solution:

f(x) → 4

degree polynomial
Let,

\;f(x)=λ(x-1)(x-2)(x-3)(x-4)+(x+1)

\;f(0)=λ(-1)(-2)(-3)(-4)+1=25

\;⇒ λ=1

\;f(5)=6+24 λ

\;\;\text " Put "\; λ=1

\;f(5)=30

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