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Differential Calculus
Aditya gurunathan
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6 May 2011 12:54:21 IST
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f(x) = f(2-x) .f(x) is a 6th degree polynomial with 4 distinct and 2 real roots.find the sum of the
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f(x) = f(2-x) .f(x) is a 6th degree polynomial with 4 distinct and 2 real roots.find the sum of the roots of f(x) = 0.


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abhishek sinha's Avatar

abhishek sinha
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9 May 2011 22:40:43 IST
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Ans : 6

From the relation , it is clear that if b is a root then 2-b is also a root. Sum of these pair of roots = 2.

There are 3 such pairs. Hence sum of the roots =6
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hemang
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10 May 2011 09:35:28 IST
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correct i think that the sum of all the roots is equal to 6.
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varun ganesh's Avatar

varun ganesh
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10 May 2011 10:02:39 IST
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 expert sirji could u please elaborate it?
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varun ganesh
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10 May 2011 10:22:21 IST
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is it f(x)*f(2-x)=f(x) ?
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abhishek sinha's Avatar

abhishek sinha
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10 May 2011 12:27:00 IST
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Clarification ....

I think ppl are confused about the problem statement ....

It is f(x)=f(2-x)

and NOT f(x)=f(2-x)*f(x)

hope this helps.
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varun ganesh's Avatar

varun ganesh
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10 May 2011 18:48:43 IST
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 then it is a reflection about x=1.which means there r 3 pairs with sum of its roots =2

so it is 6
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