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

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

A

`2p^(3) + `r = 3pq

B

`p^(3) r = q^(3)`

C

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

D

none

Text Solution

Verified by Experts

The correct Answer is:
2
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B|76 Videos

  • THEORY OF EQUATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) SET -1|5 Videos

  • THEORY OF EQUATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise SET - 4|4 Videos

  • THEORETICAL DISTRIBUTIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) CHOOSE THE CORRECT ANSWER FROM THE ALTERNATIVES 1.2.3 OR 4 GIVEN (SET -4)|5 Videos

  • TRANSFORMATION OF AXES

    DIPTI PUBLICATION ( AP EAMET)|Exercise SET-4|3 Videos

Similar Questions

Explore conceptually related problems

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

show that the condition that the roots of x^3 + px^2 + qx +r=0 may be in G.P is p^3 r=q^3

show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in A.P " is" 2p^3 -3pq +r=0

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

The condition that the roots of x^3 -bx^2 +cx -d=0 are in G.P is

If the roots of 3x^(3) - 26x^(2) + 52x - 24 = 0 are in G.P. then roots are

DIPTI PUBLICATION ( AP EAMET)-THEORY OF EQUATIONS-EXERCISE 1A
  1. The roots of x^(4) - 12x^(3) + 34x^(2) - 12x + 1 = 0 are

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. The condition that the roots of x^(3) -bx^(2) + cx - d = 0 are in geo...

    Text Solution

    |

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

    Text Solution

    |

  6. If the roots of 2x^(3) - 3x^(2) + kx + 6 = 0 are in A.P then k =

    Text Solution

    |

  7. If the roots 4x^(3) - 12x^(2) + 11x + k = 0 are in A.P. then k =

    Text Solution

    |

  8. If the roots of x^(3) - kx^(2) + 14x - 8 = 0 are in G.P. then k =

    Text Solution

    |

  9. If the roots of x^(3) - 14x^(2) + 56x + k = 0 are in G.P. then k =

    Text Solution

    |

  10. If the roots of kx^(3) -18x^(2) -36x + 8 =0 are in H.P, then k is

    Text Solution

    |

  11. Find the condition that x^3-px^2+qx-r=0 may have the sum of its roots ...

    Text Solution

    |

  12. The condition that the x^(3) -px^(2) + qx -r = 0 may be the sum of th...

    Text Solution

    |

  13. If one root of x^(3) + 3x^(2) + 5x + k = 0 may be the sum of the other...

    Text Solution

    |

  14. Let A = {:|(2,e^(ipi)),(i^(2),i^(2012))|,C =(d)/(dx) ((1)/(x))|(x=1),...

    Text Solution

    |

  15. The condition that the product of two of the roots x^3 +px^2 +qx ...

    Text Solution

    |

  16. If the product of two of the roots of x^(3) + kx^(2) - 3x + 4 = 0 may ...

    Text Solution

    |

  17. If x^(4) + px^(3) + rx + s^(2) is a perfect square then p^(3) + 8r =

    Text Solution

    |

  18. If x^(4) + px^(3) + rx + s^(2) is a perfect square then ps =

    Text Solution

    |

  19. If -1, 2 ,alpha are roots of 2x^(3) + x^(2) - 7x - 6 = 0 then alpha =

    Text Solution

    |

  20. If 1, -2, 3 are roots of x^(3) - 2x^(2) + ax + 6 = 0 then a =

    Text Solution

    |