Home
Class 11
MATHS
If p,q,r are in G.P. and the equations, ...

If p,q,r are in G.P. and the equations, `px^(2) + 2qx + r = 0 and dx^2+2ex + f = 0 ` have a common root, then show that `d/p , e/q, f/r` are in A.P.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems|13 Videos

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems -Long Answer Type Question|4 Videos

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Textbook based MCQs (Latest Exam MCQs)|3 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Question of Module)|16 Videos

  • SETS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|28 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

If the equation x^(3) +px +q =0 has three real roots then show that 4p^(3)+ 27q^(2) lt 0 .

If the equation x^(2)-px+q=0 and x^(2)-ax+b=0 have a comon root and the other root of the second equation is the reciprocal of the other root of the first, then prove that (q-b)^(2)=bq(p-a)^(2) .

If p + r = 2q and 1/q + 1/s = 2/r , then prove that p : q = r : s .

If p ,q , in {1,2,3,4}, then find the number of equations of the form p x^2+q x+1=0 having real roots.

If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^(2) – 12x + q = 0 , where a,b,c,d form a G.P Prove that (q+q):(q-p) = 17 : 15

The negation of p^^(q implies ~r) is …….

Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != 0 .If p,q,r are in A.P. and 1/alpha+1/beta=4 , then the value of |alpha-beta| is :

Let alpha,beta be the roots of the equation x^2-p x+r=0 and alpha/2,2beta be the roots of the equation x^2-q x+r=0 , the value of r is

KUMAR PRAKASHAN-SEQUENCE AND SERIES-Testbook Illustrations for Practice Work
  1. If the sum of n terms of an A.P. is nP+1/2n(n-1)Q , where P and Q are...

    Text Solution

    |

  2. The sum of n terms of two arithmetic progressions are in the ratio (3n...

    Text Solution

    |

  3. The income of a person is Rs 3,00,000 in the first year and he receive...

    Text Solution

    |

  4. Example 8 Insert 6 numbers between 3 and 24 such that the resulting se...

    Text Solution

    |

  5. Find the 10^(th) and n^(th) terms of the G.P . 5, 25,125 ................

    Text Solution

    |

  6. Which term of the G.P., 2,8,32, ... up to n terms is 131072 ?

    Text Solution

    |

  7. In a GP the 3rd term is 24 and 6th term is 192. Find the 10th term.

    Text Solution

    |

  8. Find the sum of first n terms and the sum of first 5 terms of the geom...

    Text Solution

    |

  9. How many terms of the G.P.3,(3)/2,3/4 ..........are needed to give the...

    Text Solution

    |

  10. The sum of first three terms of a G.P. is 13/12 and their product is –...

    Text Solution

    |

  11. Find the sum of the sequence 7, 77, 777, 7777, ... to n terms.

    Text Solution

    |

  12. A person has 2 parents, 4 grandparents, 8 great grandparents, and so o...

    Text Solution

    |

  13. Insert three numbers between 1 and 256 so that the resulting sequence ...

    Text Solution

    |

  14. If A.M. and G.M. of two positive numbers a and b are 10 and 8, respect...

    Text Solution

    |

  15. Find the sum to n terms of the series : 5+11+19+29+41..........

    Text Solution

    |

  16. Find the sum to n terms of the series whose n^("th") term is n (n+3).

    Text Solution

    |

  17. If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, the...

    Text Solution

    |

  18. If a, b, c are in G.P. and a^(1/x) =b^(1/y)=c^(1/z) , prove that x, y...

    Text Solution

    |

  19. If a, b, c, d and p are different real numbers such that (a^2 + b^2 + ...

    Text Solution

    |

  20. If p,q,r are in G.P. and the equations, px^(2) + 2qx + r = 0 and dx^2+...

    Text Solution

    |