JEE Class main Answered
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
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](https://images.topperlearning.com/topper/tinymce/cache/37f0ea2aa5dc283b0cd31029a1240ede.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/37f0ea2aa5dc283b0cd31029a1240ede.png)
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](https://images.topperlearning.com/topper/tinymce/cache/8e120ad1caae19b79517867d40960cd1.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/8e120ad1caae19b79517867d40960cd1.png)
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
Application Videos
Concept Videos
JEE main - Maths
Asked by yadavankith998 | 25 Jul, 2024, 22:08: PM
JEE main - Maths
Asked by sambaiahb167 | 25 Jul, 2024, 20:16: PM
JEE main - Maths
Asked by swapnanemuturi | 24 Jul, 2024, 20:17: PM
JEE main - Maths
Asked by sadhnadhagare1989 | 05 Jul, 2024, 20:06: PM
JEE main - Maths
Asked by pankajofficial | 28 Jun, 2024, 17:24: PM
JEE main - Maths
Asked by shronika | 25 Jun, 2024, 20:44: PM
JEE main - Maths
Asked by sinhashailesh349 | 25 Jun, 2024, 09:21: AM
JEE main - Maths
Asked by kumaraaditya2008 | 24 Jun, 2024, 17:19: PM
JEE main - Maths
Asked by sagnikguha2008 | 20 Jun, 2024, 10:28: AM
JEE main - Maths
Asked by pankajofficial | 20 Jun, 2024, 00:28: AM