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

If `p(x)=(1+x^2+x^4++x)/(1+x+x^2++x^(n-1)^(2n-2)` is a polynomial in `x ,t h e nn` can be `5` b. `10` c. `20` d. `17`

A

5

B

10

C

20

D

17

Text Solution

Verified by Experts

The correct Answer is:
A, D
`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`. So, n must be odd.
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MATRIX MATCH TYPE )|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Numerical)|28 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|1 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

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 n.

If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

D={x:x=2n-1<20 and n in N}

If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree- a. 2 b. \ 3 c. \ 0 d. 1

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

Let p_1(x) = x^3 – 2020x^2 + b_1x + c_1 and p_2(x) = x^3 – 2021x^2 + b_2x + c^2 be polynomials having two common roots alpha and beta . Suppose there exist polynomials q_1(x) and q_2(x) such that p_1(x)q_1(x) + p_2(x)q_2(x) = x^2 – 3x + 2 . Then the correct identity is

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If p x^4\ \ q x^3+r x^2+s x+t=|x^2+3xx-1x+3x+1 2-xx-3x-3x+4 3x|t h e n\ is equal to- a. b. c. d. none

CENGAGE-PROGRESSION AND SERIES-Exercise (Multiple & Comprehension)
  1. The tems of an infinitely decreasing decreasing G.P having common rati...

    Text Solution

    |

  2. Let a1,a2,a3…… ,an be in G.P such that 3a1+7a2 +3a3-4a5=0 Then common...

    Text Solution

    |

  3. If p(x)=(1+x^2+x^4++x)/(1+x+x^2++x^(n-1)^(2n-2) is a polynomial in x ,...

    Text Solution

    |

  4. If n >1 , the value of the positive integer m for which n^m+1 divides ...

    Text Solution

    |

  5. The next term of the G.P. x ,x^2+2,a n dx^3+10 is (729)/(16) b. 6 c. 0...

    Text Solution

    |

  6. If 1+2x +3x^2+4x^3 +…..oo ge 4 then

    Text Solution

    |

  7. Let S1, S2, be squares such that for each ngeq1, the length of a side...

    Text Solution

    |

  8. If a, b and c are in G.P and x and y, respectively , be arithmetic mea...

    Text Solution

    |

  9. Consider a sequence {an} with a1=2 & an =(a(n-1)^2)/(a(n-2)) for all ...

    Text Solution

    |

  10. The numbers 1, 4, 16 can be three terms (not necessarily consecutive) ...

    Text Solution

    |

  11. The sum of an infinite geometric series is 162 and the sum of its firs...

    Text Solution

    |

  12. If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-...

    Text Solution

    |

  13. Sum of an infinite G.P is 2 and sum of its two terms is 1.If its secon...

    Text Solution

    |

  14. For 0 lt phi lt pi//2 , if x =Sigma(n=0)^(oo) cos^(2n) phi ,y=Sigma(n...

    Text Solution

    |

  15. For the series, S=1 +(1)/(1+3)(1+2)^2+(1)/((1+3+5))(1+2+3)^2+(1)/((1...

    Text Solution

    |

  16. If Sigma(r=1)^(n) r(r+1)(2r +3)=an^4+bn^3+cn^2+dn +e then

    Text Solution

    |

  17. If Sn=1^2-2^2+3^2-4^2+5^2-6^2+ ,t h e n S(40)=-820 b. S(2n)> S(2n+2) ...

    Text Solution

    |

  18. 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+ n terms ...

    Text Solution

    |

  19. Given that x+y+z =15 when a,x,y,z,b are in A.P and 1/x+1/y+1/z=5/3 whe...

    Text Solution

    |

  20. If a, b and c are in H.P., then the value of ((ac+ab-bc)(ab+bc-ac))/(a...

    Text Solution

    |