Home
Class 11
MATHS
If a and b are the roots of x^2-3 x+p=0 ...

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

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    V PUBLICATION|Exercise QUESTIONBANK|79 Videos
  • SETS

    V PUBLICATION|Exercise QUESTION BANK|116 Videos

Similar Questions

Explore conceptually related problems

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

If a, b are the roots of x^(2)+px+1=0 and c, d are the roots of x^(2)+qx+1=0 , show that q^(2)-p^(2)=(a-c)(b-c)(a+d) (b+d) .

If (x+1) and (x -1) are factors of x^3+2x^2 + px + q , find p and q.

If c, d are the roots of the equation (x-a) (x-b) - k=0 , then prove that a, b are the roots of the equation (x-c) (x-d) + k= 0

If the roots of the equation x^(2) + px + c =0 are 2,-2 and the roots of the equation x^(2) + bx + q=0 are -1,-2 , then the roots of the equation x^(2) + bx + c =0 are

V PUBLICATION-SEQUENCES AND SERIES-QUESTIONBANK
  1. If a (1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P. Prove that a, b, c ...

    Text Solution

    |

  2. If a, b, c, d are in G.P. Prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are...

    Text Solution

    |

  3. If a and b are the roots of x^2-3 x+p=0 and c and d are roots of x^2-1...

    Text Solution

    |

  4. If A and G be A. M and G. M respectively between two positive numbers....

    Text Solution

    |

  5. If a, b, c are in A.P, b, c, d are in G.P. and 1/c , 1/d,1/e are in A....

    Text Solution

    |

  6. Find the sum to n terms of the series: 5+55+555+………..

    Text Solution

    |

  7. Find the 20^( th) term of the series 2 xx 4+4 xx 6+6 xx 8+. . .,+ n t...

    Text Solution

    |

  8. Find the sum of the first n terms of the series : 3+7+13+21+31+. . .

    Text Solution

    |

  9. If S1, S2, S3 are the sum of first n natural numbers, their squares an...

    Text Solution

    |

  10. Find the sum to n terms of the series: (1^3)/(1)+(1^3+2^3)/(1+3) + ...

    Text Solution

    |

  11. Show that (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. .+n...

    Text Solution

    |

  12. A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and...

    Text Solution

    |

  13. Shamshad Ali buys a scooter for Rs. 22000. He pays Rs. 4000 cash and a...

    Text Solution

    |

  14. A person writes a letter to four of his friends. He asks each one of t...

    Text Solution

    |

  15. A man deposited Rs. 10000 in a bank at the rate of 5 % simple interest...

    Text Solution

    |

  16. A manufacturer reckons that the value of a machine, which costs him Rs...

    Text Solution

    |

  17. 150 workers were engaged to finish a job in a certain number of days. ...

    Text Solution

    |

  18. Write the first 'three terms of the sequences whose nth term Tn is giv...

    Text Solution

    |

  19. Show that the sequence: log a, log ((a^2)/b), log(( a^3)/(b^2)) . . is...

    Text Solution

    |

  20. Which term of the sequence 37,32,27,22,... is -103

    Text Solution

    |