Home
Class 11
MATHS
Prove that p + q = 0 " if " x^(3) - 3px ...

Prove that `p + q = 0` " if " `x^(3) - 3px + 2q`" is divisible by" `(x + 1)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
`thereforep+q=0`
Promotional Banner

Topper's Solved these Questions

  • BASIC ALGEBRA

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 2.1|5 Videos
  • BASIC ALGEBRA

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 2.2|9 Videos
  • BINOMIAL THEOREMN,SEQUENCES AND SERIES

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE(Choose the correct option for the following)|31 Videos

Similar Questions

Explore conceptually related problems

Prove that ap+q=0 if f(x)=x^3-3px+2q is divisible by g(x)=x^(2)+2ax+a^(2).

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

Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisible by x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot

The sum of the polynomials p(x) = x^(3) - x^(2) - 2, q(x) = x^(2) - 3x + 1

Prove that p x^(q-r)+q x^(r-p)+r x^(p-q)> p+q+r ,w h e r ep ,q ,r are distinct and x!=1.

If the roots of the equadratic equation x^(2) + px + q = 0 " are " tan23^(@) "and" tan22^(@), then find the value of q - p .

If the quotient obtained on dividing ( 8 x^(4) - 2x^(2) + 6x-7) by ( 2x + 1 ) is ( 4x^(3) + px^(2) - qx + 3 ) , then find p,q and also the remainder.

Let P(x) = 4x^(2) - 3x + 2x^(3) + 5 and q(x) = x^(2) + 2x + 4 find p ( x) - q(x) .

PREMIERS PUBLISHERS-BASIC ALGEBRA-PROBLEMS FOR PRACTICE I -Choose the correct option for the following(MCQ)
  1. Prove that p + q = 0 " if " x^(3) - 3px + 2q" is divisible by" (x + 1)...

    Text Solution

    |

  2. Solve 2|x - 5|+ 5 = 21

    Text Solution

    |

  3. x le 6 and x ge - 2 is given by interval notation as

    Text Solution

    |

  4. A cubic equation has roots 2 and 1+ sqrt3 Then its equation is

    Text Solution

    |

  5. If x^(2)-6x+k = 0 has equal roots the value of k is

    Text Solution

    |

  6. The solution set for the inequality2x^(2)+5x-3is

    Text Solution

    |

  7. If a and b are the roots of the equation x^(2)- kx + 9 = 0 and satisfy...

    Text Solution

    |

  8. The solution set of the following inequality |x - 1| le |x - 3| is

    Text Solution

    |

  9. sqrtp (where p is a prime number) is

    Text Solution

    |

  10. log(2)4+ log(4)4 + log(16)4 is equal to

    Text Solution

    |

  11. (x^(8)y^(4))^((1)/(4))

    Text Solution

    |

  12. Match the following

    Text Solution

    |

  13. Find the incorrect statement in the following.

    Text Solution

    |

  14. Find the incorrect statement in the following

    Text Solution

    |

  15. Find the correct statement in the following

    Text Solution

    |

  16. Find the correct statement in the following

    Text Solution

    |

  17. Find the incorrect statement in the following

    Text Solution

    |

  18. Find the odd one out The inequalities -3x gt 0 or 3x - 4 lt 11 is repr...

    Text Solution

    |

  19. Find the odd one out with respect to root of

    Text Solution

    |

  20. Find the odd one out from the following

    Text Solution

    |

  21. Assertion: The equation x^(2)+|x-1|=1two solutions. Reason: |x| = x if...

    Text Solution

    |