Home
Class 12
MATHS
If p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2+...

If `p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1))` is a polomial in `x` , then find possible value of `ndot`

Text Solution

Verified by Experts

The correct Answer is:
n is odd
`p(x)=((1-x^(2n))/(1-x^(2)))((1-x)/(1-x^(n))=(1+x^(n))/(1+x))`
As p(x) is a polynomial , x=-1 must be a zero of `1+x^(n)`, i.e., `1+(-1)^(n)=0`. Hence, n is odd.
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.6|11 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.7|4 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.4|13 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

If x gt 0 , (x^(n))/(1+x+x^(2)+...+x^(2n)) is

If lim_(x->2)(x^n-2^n)/(x-2)=80 and n in N ,then find the value of n.

Find all possible values of (x^2+1)/(x^2-2) .

If 2x + 1/x = 2, then find the value of (x)/(2x^2+x+1) .

If sin^(-1)((4x)/(x^2+4))+2tan^(-1)(-x/2) is independent of x , find the values of x

If the middle term in the expansion of (x^2+1//x)^n is 924 x^6 , then find the value of ndot

If y=(1+x)(1+x^2)(1+x^4)...(1+x^(2^n)) then (dy)/(dx) at x=0 is

If int (2x^(3)-7x+2)/(x^(3)+2x^(2)) dx = 2x - n log |x| - 1/x +c then the value of n is -

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n) , then find the value of C_(0)+C_(2)+C_(4)+C_(6)+........ ​ ​