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If p(x)=(1+x+x^2+x^3+........+x^(2n-2))/(1+x+x^2+......x^(n-1)) is a polynomial in x,then find possible value of n.
Asked by Vidushi412 | 21 Jan, 2019, 09:56: AM
answered-by-expert Expert Answer
we have begin mathsize 12px style 1 space plus x space plus x squared space plus x cubed plus............. plus x to the power of n minus 1 end exponent space equals space fraction numerator 1 minus x to the power of n over denominator 1 minus x end fraction end style
hence begin mathsize 12px style fraction numerator 1 plus x plus x squared plus.............. plus x to the power of 2 n minus 2 end exponent over denominator 1 plus x plus x squared plus.............. plus x to the power of n minus 1 end exponent end fraction space equals space fraction numerator 1 minus x to the power of 2 n minus 1 end exponent over denominator 1 minus x to the power of n end fraction end style
from the above exprtession, it will be seen that polunomial is possible only if n = 1
Answered by Thiyagarajan K | 21 Jan, 2019, 12:44: PM

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