Home
Class 11
MATHS
The polynomial x^6+4x^5+3x^4+2x^3+x+1 is...

The polynomial `x^6+4x^5+3x^4+2x^3+x+1` is divisible by

A

`x+omega`

B

`x+omega^2`

C

`(x+omega)(x+omega^2)`

D

`(x-omega)(x-omega^2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

Determine the value of k for which the polynomial (2x^(4)-3x^(3)-x^(2)+x+k) is divisible by (2x - 1).

Determine the value of k for which the polynomial (2x^(4)-3x^(3)-x^(2)+x+k) is divisible by (2x + 3).

The polynomial x^3 + 3x^2 - x - 3 is divisible by

If the polynomial p(x)=x^(3)+6x^(2)+4x+k is divisible by (x + 2), then k =

If the polynomial x^(4)-6x^(3)-16x^(2)+25x+10 is divided by another polynomial x^(2)-2x+k , the remainder comes out to be x+a , find k and a.

Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is divisible by x^2 + 1 , then

If the polynomial f(x)=2x^(3)+kx^(2)+11x+k+3 be divisible by (2x - 1), then the value of k =

Find the value of k if the polynomial p(x)=2x^(4)+3x^(3)+2kx^(2)+3x+6 is divisible (x + 2).

If the polynomial p(x)=x^(4)-a^(2)x^(2)+2x-a be divisible by (x + a), then calculate the value of a.

If the polynomial x^(4)-2x^(3)+3x^(2)-ax+b be divided by (x -1) and (x + 1), the respective remainders are 5 and 19. Determine the remainder when the polynomial is divided by (x + 2).

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. A man walks a distance of 3 units from the origin towards the north ea...

    Text Solution

    |

  2. z^2+zabsz+absz^2=0 then the locus of z is

    Text Solution

    |

  3. The polynomial x^6+4x^5+3x^4+2x^3+x+1 is divisible by

    Text Solution

    |

  4. If z1,z2,z3 are three complex numbers and A= abs[[argz1,argz2,argz3],...

    Text Solution

    |

  5. If abs(z-i)le2 and z0=5+3i then the maximum value of abs(absiz+z0) is

    Text Solution

    |

  6. If z(Re z ne2) be a complex number such that z^2-4z=absz^2+16/absz^3 t...

    Text Solution

    |

  7. Let z=x+iy be a complex number where x and y are integers then the are...

    Text Solution

    |

  8. If z and w are two nonzero complex numbers such the abs(zw)=1 and arg...

    Text Solution

    |

  9. if log(1/2)(( absz^2+2absz+4)/(2absz^2+1))lt0 then the region traced b...

    Text Solution

    |

  10. If abs(z-2-i)=abszabssin(pi/4-argz) then locus of z is

    Text Solution

    |

  11. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

    Text Solution

    |

  12. If z=iloge(2-sqrt3) then the value of cosz

    Text Solution

    |

  13. If alpha is the nth root of unity then 1+2alpha+3alpha^2+….to n terms ...

    Text Solution

    |

  14. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

    Text Solution

    |

  15. If alpha=cos((8pi)/11+isin((8pi)/11 then Re(alpha+alpha^2+alpha^3+alph...

    Text Solution

    |

  16. If z be any complex number such that abs(3z-2)+abs(3z+2)=4 then locus ...

    Text Solution

    |

  17. x^(3m)+x^(3n-1)+x^(3r-2) where m,n,r in N is divisible by

    Text Solution

    |

  18. A fourth root of -1 is

    Text Solution

    |

  19. If z1=a+ib and z2=c+id are complex numbers such that abs(z1)=abs(z2)=1...

    Text Solution

    |

  20. Let z1 and z2 be complex numbers such that z1 nez2 and absz1=absz2 if ...

    Text Solution

    |