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If f(x) is a polynomial of degree four ...

If f(x) is a polynomial of degree four with leading coefficient one satisfying `f(1)=1, f(2)=2,f(3)=3`.then `[(f(-1)+f(5))/(f(0)+f(4))]`

A

`4`

B

`5`

C

`6`

D

`7`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` According to question
`f(x)-x=(x-1)(x-2)(x-3)(x-alpha)`
`implies f(-1)=24(1+alpha)-1`
`f(0)=6alpha`
`f(4)=6(4-alpha)+4`
`f(5)=24(5-alpha)+5`
`implies[(f(-1)+f(5))/(f(0)+f(4))]=[(148)/(28)]=5`
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