Question

If ƒ(x) is polynomial of degree 4 such that ƒ(1) = 1, ƒ(2) = 2, ƒ(3) = 3, ƒ(4) = 4 & ƒ(0) = 1

find​

Answer 1

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Answer 2

Answer:

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If f(x) is the polynomial of degree 4 with leading co efficient one satisfying f(1) = 1 , f(2) =2 , f(3) =3 then [

f(0)+f(4)

f(−1)+f(5)

]

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Answer

Correct option is

C

1

f(x)=x for x∈1,2,3

f(x)−x=0 for x∈1,2,3

∴f(x)−x=(x−1)(x−2)(x−3)

f(x)=(x−1)(x−2)(x−3)+x

f(−1)=−25

f(5)=29

f(0)=−6

f(4)=10

f(0)+f(4)

f(−1)+f(5)

=

−6+10

−25+29

=

4

4

=1