Home
Class 12
MATHS
Let x(1), x(2) be the roots of the equat...

Let `x_(1), x_(2)` be the roots of the equation `x^(2)-3 x+p=0` and let `x_(3), x_(4)` be the roots of the equation `x^(2)-12 x+q=0` . If the numbers `x_(1), x_(2) x_(3), x_(4)` (in order) form an increasing G.P. then,

A

`p=2, q=16`

B

`p=2, q=32`

C

`p=4, q=16`

D

`p=4, q=32`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos

  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

Roots of the equation x^(2) -2x+ 1 =0 are :

The roots of the equation x^(2)-2sqrt(3)x+3=0 are

If p and q are the roots of the equation x^(2)+p x+q=0 then

Roots of equation x^(2)-2x+1=0 are:

The roots of the equation 12 x^2 + x - 1 = 0 is :

If p and q are the roots of the equation x^2-p x+q=0 , then

If x_1, x_2 be the roots of the equation x^2 -3x+ A=0 and x_3,x_4 be those of the equation x^2-12x + B = 0 and x_1 , x_2, x_3, x_4 be an increasing GP. find find A and B.

The sum of the real roots of the equation x^(2)+|x|-12=0 is

Verify whether 1 and (3)/(2) are the roots of the equation 2x^(2)-5x+3=0

Find the roots of the quadratic equation x^(2)+7x+12=0

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. If a, b, c are positive real numbers, then the number of real roots of...

    Text Solution

    |

  2. The value of 'a' for which the equation x^(3) + ax + 1 = 0 and x^(4) +...

    Text Solution

    |

  3. If alpha and beta are the roots of x^(2) + qx + 1 = 0 and gamma, delt...

    Text Solution

    |

  4. If a,b,c are in G.P.L, then the equations ax^(2) + 2bx + c = 0 0 and d...

    Text Solution

    |

  5. Let x(1), x(2) be the roots of the equation x^(2)-3 x+p=0 and let x(3)...

    Text Solution

    |

  6. Both the roots of the equation : (x - b) (x -c) + (x - c) (x - a) +...

    Text Solution

    |

  7. If x^(2)+x+1 is a factor of a x^(3)+b x^(2)+c x+d, then the real root ...

    Text Solution

    |

  8. If a le 0 then the real values of x satisfying x^(2)-2 a|x-a|-3 a^(2)=...

    Text Solution

    |

  9. If x^(2)-3 x+2 is a factor of x^(4)-p x^(2)+q, then the values of p an...

    Text Solution

    |

  10. If the equations x^(2)+b^(2)=1-2b x and x^(2)+a^(2)=1-2 a x have one a...

    Text Solution

    |

  11. If the product of the roots of the equation x^(2) - 3kx + 2e^(2 log k)...

    Text Solution

    |

  12. Let a, b, c be real. If a x^(2)+b x+c=0 has two real roots alpha and...

    Text Solution

    |

  13. Let (sin a) x^(2)+(sin a) x+(1-cos a)=0 . The set of values of a for w...

    Text Solution

    |

  14. If p, q, are real and p ne q then the roots of the equation (p-q) x^(...

    Text Solution

    |

  15. The value of ' c ' for which |alpha^(2)-beta^(2)|=(7)/(4) where alpha ...

    Text Solution

    |

  16. If alpha, beta are the roots of the equation λ (x^(2)-x)+x+5=0 and if ...

    Text Solution

    |

  17. If alpha and beta are the rotos of a x^(2)+b x+c=0 the equation whose ...

    Text Solution

    |

  18. If alpha, beta are the rots of a x^(2)+b x+c=0 and alpha+h, beta+h are...

    Text Solution

    |

  19. If x^(2) + ax + b = 0 and x^(2) + bx + a = 0 have a common root, then...

    Text Solution

    |

  20. The minimum value of 2 x^(2)+x-1 is

    Text Solution

    |