11Hello??? pls reply.. :(
Pls post solution of test which you posted (T-276). plzzzzzzzzzzzzz. :)
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23 Answers
1test 277 is awesum.................... it has nothing to do wid studies, only smartness...........hehehe
and nishu bhaiyya tht test was a joke actually........
he gave d initial condition as 1=5.......so at d end he used tht and confused us..........and i kno u got extremely angry at such an illogical ques...........hehe but nice one santom........
341You must read it along with Post 14. here f(x) is such that whenever f(x) = 0, xnf(1/x) = 0.
Then the rest of the post holds.
21Prophet Sir,
Can u pl. explain the "k" factor that u introduced??? I read ur post 19 but still not getin [2]
I took f(x) = x2.........(==> n =2)........ (==> roots= 0)
then f(1/x) = 1/x2
==> x^n f(1/x) = x^2/x^2 = 1....
but thn. roots differ [2] [2]
1great sir why cant we think like u...!!!!!! simply "where did u take coaching ;)"
341See whenever f(x) = 0 we also have f(1/x) = 0 or xn f(1/x) = 0.
Both f(x) and xnf(1/x) are polynomials of degree n (In fact xnf(1/x) is the polynomial obtained by reversing the order of f(x). Like 2x2+x+3 will become 3x2+x+2. Mirror image)
This means they have the same set of roots.
1@ prophet,
That means, the roots of f(x) and xnf(1/x) are the same
will u pls explain this line?
341We are given f(x) + f(1/x) = f(x) f(1/x)
Suppose f(x) = c ( a constant), then c = 0 or 2
Now if f(x) is not a constant:
Note that whenever f(x) = 0 we must have f(1/x) = 0 from the above relation.
That means, the roots of f(x) and xnf(1/x) are the same
So, we can write xn f(1/x) = k f(x)
Now multiplying the given relation by xn we get
xn f(x) + xnf(1/x) = f(x) xn f(1/x) or
xn f(x) + k f(x) = k f2(x) or
f(x) = xn/k + 1
Putting this form of the function into the given relation, we get k = 1 or k = -1
Hence if f(x) is not a constant, f(x) = 1+xn or 1-xn
62If santom does not reply.. I will delete that test..
it is Not upto my liking and quality!
There are a couple others that need to go!
11i didn't get how he got xn+1 as a solution. I actually got the full 5 marks in this test by guessing the ans! ;p
62Sorry Santom.. i meant test 277..
I could nto many any sense of it.. could you explain that one too?
1sorry . posting now
f(x)+f(1/x)=f(x)f(1/x)
(f(x)-1)(f(1/x)-1)=1
implies
f(x)=xn+1
f(4)=17 implies n=2;
->f(7)=50.