1the ques is the same else i don't know....
Let the P(x) be a polynomial of degree 11 such that P(x)= 1/(x+1), for x= 1,2,....11.
The Value of P(12) is.....
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15 Answers
3hey prateek shud i need to expand the P(X) using binomial upto degree 11,or is there any rong in the qn.
1ajeeb hai wais edekhe toh answer a lagta hai bt if that wud hav had been d case u wud hav had nt asked d q :P
341If the polynomial is of degree 11, then the value of the polynomial should be known at 12 values of x, for the polynomial to be fully determined. Please check the question.
66Insufficient Information
The given information implies that the numbers 1,2,3,...., 11 are the roots of the 12th degree polynomial
f(x)=(x+1) P(x) - 1
Let the last root be k.
Then, f(x) can be factorized as
f(x)=a(x-1)(x-2)(x-3)....(x-11)(x-k)
i.e.
(x+1) P(x) -1 = a(x-1)(x-2)(x-3)....(x-11)(x-k)
The above being true for all x, setting x=-1 gives
-1=(-1)12 12! (1+k)a
Now from here onwards we cannot determine the two unknowns unless one more piece of info is provided.
For example, if the question said "monic polynomial", then a = 1 and so k is determined. And hence the polynomial is uniquely known.
I don't think we can get the values of a and k if no more info is given.
24yeah kayamant sir is rite.........the ques is incomplete....thats why no one was able to answer it