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Q.

Let fN(x) be a polynomial function which satisfies  f1(x)=n=1N(x-n)n If n1 is sum of all values of x for which f10(x) attains maxima and n2denotes the sum of values x for which  f10(x) attains minima while n3 stands for sum of value of x at which inflexion point occurs then the value of 6(n1+n2)n3is 

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answer is 5.

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Detailed Solution

f10(x)=(x1)(x2)2(x3)3(x10)10

f10(x)>0(x1)(x3)(x5)(x7)(x9)>0

Points of maxima = 3,7                                  n1 = 10

Points of minima = 1, 5, 9                   n2 = 15

Points of inflexion = 2, 4, 6, 8, 10       n3 = 30

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