Home
Class 12
MATHS
The condition that the roots of x^3 +3 p...

The condition that the roots of `x^3 +3 px^2 +3qx +r = 0` may be in `H.P.` is

A

`2p ^(3) -3pqr + r ^(2) =0`

B

`3p 6(3) -2pqr+p^(2) =0`

C

`2q ^(3) -3pqr+ r ^(2)=0`

D

`r ^(3) +3pqr+2q ^(3) =0`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|44 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|23 Videos

  • PROBABILITY

    VK JAISWAL|Exercise Exercise -5 : Subjective Type problems|12 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

The condition that the roots of x^(3)+3px^(2)+3qx+r=0 may be in H.P. is

The condition that the roots of x^(3)+3px^(2)+3qx+r=0 may be in G.P. is

The condition that the roots of x^(3)px^(2)+qx-r=0 may be in G.P. is

FIND that condition that the roots of equation ax^3+3bx^2+3cx+d=0 may be in G.P.

The condition that the product of two of the roots of x^(3)+px^(2)+qx+r=0 may be -1 is

The condition that one root of px^(2)+qx+r=0 may be double of the other is

Find the condition that the zeros of the polynomial f(x)=x^(3)+3px^(2)+3qx+r may be in A.P.

VK JAISWAL-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The condition that the roots of x^3 +3 px^2 +3qx +r = 0 may be in H.P....

    Text Solution

    |

  2. Let f(x) = ax^2 + bx + c where a,b,c are integers. If sin\ pi/7 * sin\...

    Text Solution

    |

  3. Let a, b, c, d be distinct integers such that the equation (x - a) (x ...

    Text Solution

    |

  4. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=(1), wher...

    Text Solution

    |

  5. The number of positive integral values of m, m le 16 for which the equ...

    Text Solution

    |

  6. If the equatio (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then ...

    Text Solution

    |

  7. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

    Text Solution

    |

  8. The integral values of x for which x^2 +17x+71 is perfect square of a ...

    Text Solution

    |

  9. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

    Text Solution

    |

  10. The number of real values of 'a' for which the largest value of the fu...

    Text Solution

    |

  11. The number of all values of n, (whre n is a whole number ) for which t...

    Text Solution

    |

  12. The number of negative intergral values of m for which the expression ...

    Text Solution

    |

  13. If the expression ax ^(4)+bx^(3)-x ^(2)+2x+3 has the remainder 4x +3 w...

    Text Solution

    |

  14. The smallest value of k for which both the roots of the equation x^2-8...

    Text Solution

    |

  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

    Text Solution

    |

  17. The curvey y = (a +1) x ^(2) + 2 meets the curve y = ax +3, a ne -1 in...

    Text Solution

    |

  18. Find the number of integral vaues of 'a' for which the range of functi...

    Text Solution

    |

  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

    Text Solution

    |

  20. Let p (x) be a polynomial equation of least possible degree, with rati...

    Text Solution

    |

  21. The range of values k for which the equation 2 cos ^(4)x-sin ^(4)x +k=...

    Text Solution

    |