plz solve the query & give its xplanation

Asked by  | 7th Sep, 2008, 09:35: AM

Expert Answer:

f(x)=x3+x2 +x=x(1+x+x2 )

Solutions of f(x)=0 are 0,w,w2

F(x)=(x+1)n -xn -1

F(0)=1n -1=0

F(w)=(w+1)n -wn -1=(-w2 )n -w-1=(-1)n w2n -wn -1

For given n,

F(w)=-(w2n +wn +1)=0, for n=3m-1 or 3m-2.

Siilarily,

F(w2 )=0

Hence (x+1)n -xn -1 is divisible by x3+x2 +x, for given values of n.

Answered by  | 15th Jun, 2009, 12:19: AM

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