Home
Class 9
MATHS
The polynomial (x^(3)+px^(2)-x+q) is div...

The polynomial `(x^(3)+px^(2)-x+q)` is divisible by `(x^(2) - 1)` and when it is divided by (x - 2), the remainder is 15. Find the values of p and q.

Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.1|57 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.2|45 Videos

  • LOGARITHM

    CALCUTTA BOOK HOUSE|Exercise Exercise - 7 (Long-answer type questions)|49 Videos

  • PROBABILITY

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 2|16 Videos

Similar Questions

Explore conceptually related problems

If the polynomial p(x)=4x^(3)-px^(2)+x-q be divided by (x - 1) and (x + 2), the respective remainders are 0 and 3. Find the value of p and q.

If the polynomial P(a)=x^(2)-2x+a be divided by (x - 3), the remainder is 0. Then a =

The polynomial (px^(2)+qx+r) is divisible by (x^(2)-1) and if x = 0, the value of the polynomial is 2. Determine the values of p, q and r.

If the polynomials x ^(3) + ax ^(2) + 5 and x ^(3) - 2x ^(2)+a are divided by (x +2) leave the same remainder. Find the value of a.

If the polynomial f(x)=2x^(3)+ax^(2)+bx-2 be divided by (2x - 3) and (x - 1), the respective remainders are 30 and 0. Calculate the values of a and b.

Polynomial P(x) contains only terms of odd degree. when P(x) is divided by (x - 3) , the ramainder is 6 . If P(x) is divided by (x^(2) - 9) then remainder is g(x) . Then find the value of g(2) .

If the polynomial p(x)=x^(3)+3x^(2)+3x+1 be divided by (x-pi) , the remainder is

If the polynomials f(x)=ax^(2)-3x+5andg(x)=x^(2)-2x+2a be divided by (x - 3) the respective remainders are same. Find the value of a.

When the polynomial 5x^3+M x+N is divided by x^2+x+1, the remainder is 0. Then find the value of M+Ndot

When a polynomial 2x ^(3) + 3x ^(2) + ax + b is divided by (x-2) leaves remainder 2, and (x +2) leaves remainder -2. Find a and b.

CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.4
  1. The polynomial (x^(3)+px^(2)-x+q) is divisible by (x^(2) - 1) and when...

    Text Solution

    |

  2. If p(x) be a polynomial such that p(-a/b)=0, then one of the factor of...

    Text Solution

    |

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

    Text Solution

    |

  4. If (x - a) be a factor of f(x), but is not a factor of g(x), where bot...

    Text Solution

    |

  5. If (x^(2)-1) be a factor of the polynomial f(x)=ax^(4)+bx^(3)+cx^(2)+d...

    Text Solution

    |

  6. (x + a) will be a factor of the polynomial p(x)=x^(n)+a^(n), when-

    Text Solution

    |

  7. If x be a factor of the polynomial f(x) = (x - a) (x + b) (x - c), the...

    Text Solution

    |

  8. If (x+sqrt11) be a factor of f(x)=x^(3)+k, then k =

    Text Solution

    |

  9. If (x^(2)+r) be a factor of the polynomial f(x)=x^(3)-rx^(2)+rx-r^(2),...

    Text Solution

    |

  10. If f(x)=2x^(3)+9x^(2)+x+k and g(x) = x -1 be two polynomials, then g(x...

    Text Solution

    |

  11. Which one of the followings is a factor of the polynomial p(x)=x^(4)-1...

    Text Solution

    |

  12. Find the value of a if (1 - 2x) is a factor of the polynomial (2x^(4)-...

    Text Solution

    |

  13. Find the value of k if (x - 2) is a factor of the polynomial (2x^(5)-6...

    Text Solution

    |

  14. If (x + 1) be a factor of the polynomial (x^(43)+kx+2), determine the ...

    Text Solution

    |

  15. If (x + 1) be a factor of the polynomial (x^(200)+2x^(201)+k), then de...

    Text Solution

    |

  16. If n be an odd negative integer, then prove that (x + 1) is a polynomi...

    Text Solution

    |

  17. Prove that the polynomial (x^(5)-y^(5)) is not divisible be (x + y).

    Text Solution

    |

  18. Is the polynomial (x^(101)+1) divisible by (x + 1) ? Give reasons in f...

    Text Solution

    |

  19. Examine whether (x + y) is a factor of the polynomial (x^(11)+y^(11)) ...

    Text Solution

    |

  20. If (x + 2y) be a factor of the polynomial (x^(2)+4xy+4y^(2)), find the...

    Text Solution

    |

  21. If (x-sqrt11) be a factor of the polynomial of f(x), but not a factor ...

    Text Solution

    |