﻿ If  f (x) is a polynomial satisfying f (x). f (1/x) = f (x) + f (1/x), and f (3) = 28, then f (4) is given by   : Kaysons Education

# If  f (x) Is A Polynomial Satisfying f (x). f (1/x) = f (x) + f (1/x), And f (3) = 28, Then f (4) Is Given By

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## Question

### Solution

Correct option is

65

By considering a general nth degree polynomial and writing the

expression  (x). (1/x) = (x) + (1/x) in terms of it, it can be

proved by comparing the coefficients of xxn-1,… and the constant term, that the polynomial satisfying the above equation is either of the form x+1 or –x+ 1. Now, from (3) = 3+1 = 28

We get 3n = 27, or n = 3. But f (3) = –3+1 = 28 is not possible, as –3n= 27 is not true for any value of n. Hence f (4) = 4+ 1 = 65.

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