Home
Class 11
MATHS
It is given that n is an odd integer gre...

It is given that n is an odd integer greater than 3 but n is not a multiple of 3 prove that `x^3+x^2+x` is a factor of `(x+1)^n-x^n-1:`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

It is given that n is an odd integer greater than 3 but n is not multiple of 3. prove that (x^(3)+x^(2)+x) is a factor of (1+x)^(n)-x^(n)-1 .

Show that if n be odd, x + 1 is a factor of x^n + 1 .

Determine whether n is an add or even positive integer, when (x + 1) is a factor of (x^(n)-1) .

If n be any positive integer (even or odd), prove that (x - y) is a factor of the polynomial x^(n)-y^(n) .

If n be an odd negative integer, then prove that (x + 1) is a polynomial of degree (x^(n)+1) .

If n be a positive integer greater than 1, prove that (frac(n+1)(2))^n > n

Show that, if n be any positive integer greater than 1, then (2^(3n) - 7n - 1) is divisible by 49.

If n is a positive integer then the coefficient of x ^(-1) in the expansion of (1+x) ^(n) (1+ (1)/(x)) ^(n) is-

'Prove that the co-efficient of x^n of the expansion of (1+x)^(2n) is the double of the coefficient of x^n of the expansion of '(1+x)^(2n-1)'

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Multiply: (2+5i)(4-3i)

    Text Solution

    |

  2. Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R. Then (a) ...

    Text Solution

    |

  3. It is given that n is an odd integer greater than 3 but n is not a mul...

    Text Solution

    |

  4. If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imagi...

    Text Solution

    |

  5. Find the complex number omega satisfying the equation z^3=8i and lyi...

    Text Solution

    |

  6. If the expression [m x-1+(1//x)] is non-negative for all positive real...

    Text Solution

    |

  7. When the polynomial 5x^3+M x+N is divided by x^2+x+1, the remainder is...

    Text Solution

    |

  8. x1 and x2 are the roots of a x^2+b x+c=0 and x1x2<0. Roots of x1(x-x2)...

    Text Solution

    |

  9. ifomegaa n domega^2 are the nonreal cube roots of unity and [1//(a+ome...

    Text Solution

    |

  10. If a ,b ,c ,d are four consecutive terms of an increasing A.P., then t...

    Text Solution

    |

  11. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

    Text Solution

    |

  12. If roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-...

    Text Solution

    |

  13. If z1, z2, z3 are three nonzero complex numbers such that z3=(1-lambda...

    Text Solution

    |

  14. Coefficient of x^99 in the polynomial (x-1) (x-2)....(x-100) is

    Text Solution

    |

  15. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

    Text Solution

    |

  16. Fill in the blanks If 2+isqrt(3) is a root of the equation x^2+p x+q=0...

    Text Solution

    |

  17. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

    Text Solution

    |

  18. Fill in the blanks. If the product of the roots of the equation x^2-3k...

    Text Solution

    |

  19. Solve for z : z^2-(3-2i)z=(5i-5)dot

    Text Solution

    |

  20. If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then ...

    Text Solution

    |