CBSE Class 11-science Answered
plz solve the query & give its xplanation
Asked by | 07 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 -wn -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 | 15 Jun, 2009, 12:19: AM
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