Home
Class 12
MATHS
If p,q,r , three positive real numbers a...

If p,q,r , three positive real numbers are in A.P., then the roots of `px^(2) + qx + r = 0` are all real for `:`

A

`|((r )/( p )) - 7| ge 4 sqrt( 3)`

B

`|(p)/( r ) - 7|lt 4 sqrt( 3)`

C

All p and r

D

No p and r

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise LATEST QUESTIONS|11 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos

  • RELATIONS

    MODERN PUBLICATION|Exercise RCQS|6 Videos

  • SETS

    MODERN PUBLICATION|Exercise Recent Competitive Questions (RCQs)|6 Videos

Similar Questions

Explore conceptually related problems

If a,b,c are positive real numbers, then the roots of the equation ax^(2) + bx + c =0

If p, q, r are real numbers then:

If p,q,r are in A.P. and are positive, the roots of the quadratic equation px^(2) + qx + r = 0 are real for :

If three positive real numbers a,b,c are in A.P. such that abc=4, then the minimum value of b is

If a, b, c are positive real numbers, then the number of real roots of the equation a x^(2)+b|x|+c=0 is

If p, q, are real and p ne q then the roots of the equation (p-q) x^(2)+5(p+q) x-2(p-q)=0 are

Value of x in the equations px^(2) + qx+r =0 is :

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

If p and q are positive real number such that p^(2) + q^(2) = 1 , then the maximum value of (p + q) is :

MODERN PUBLICATION-SEQUENCES AND SERIES -MCQ ( Level-II)
  1. If a,b,c are digits, then the rational number represented by 0.c ab ab...

    Text Solution

    |

  2. If I(n) = int(0)^(n) ( 1- sin 2nx)/( 1-cos 2n)dx then I(1) , I(2) , I(...

    Text Solution

    |

  3. If p,q,r , three positive real numbers are in A.P., then the roots of ...

    Text Solution

    |

  4. If a(1),a(2) , a(3),"……..",a(n) are in H.P. , then : (a(1))/( a(2) ...

    Text Solution

    |

  5. The value of sum(r=1)^(n) log ((a^(r ))/( b^(r-1))) is :

    Text Solution

    |

  6. If a(1) , a(2),"………",a(n) are n non-zero real numbers such that ( a(1)...

    Text Solution

    |

  7. The sum of n terms of the series : (1)/( 1.2.3.4) + ( 1)/( 2.3.4.5) ...

    Text Solution

    |

  8. If sum(r=1)^(prop) t(r ) = ( n (n +1) ( n + 2) ( n + 3))/( 8 ) , wher...

    Text Solution

    |

  9. sum(i=1)^(n) sum(j=1)^(i)sum(k=1)^(j) 1 equals :

    Text Solution

    |

  10. If log(x)a,a^(x//2) and log(b)x are in G.P., then x equals :

    Text Solution

    |

  11. If x,y,z are in A.P. and tan^(-1)x , tan^(-1)y and tan^(-1) z are als...

    Text Solution

    |

  12. If P,Q,R be the A.M., G.M., H.M. respectively between any two rational...

    Text Solution

    |

  13. Let S = ( 8 ) /( 5) + ( 16)/( 65) +"...." + ( 128)/( 2^(18) + 1) , th...

    Text Solution

    |

  14. The sides a,b,c of Delta ABC are in G.P. , where log a - log 2b, log ...

    Text Solution

    |

  15. Let alpha, beta be the roots of x^(2) -x + p = 0 and gamma , delta b...

    Text Solution

    |

  16. If the sum of the first 2n terms of the A.P. 2,5,8,"……….." is equal to...

    Text Solution

    |

  17. The first term of a G. P. is 1. The sum of the third and fifth terms i...

    Text Solution

    |

  18. Suppose a,b,c are in A.P. and a^(2) , b^(2) , c^(2) are in G.P. If a ...

    Text Solution

    |

  19. If sum of the roots of the quadratic equation ax^(2) + bx+c = 0 is equ...

    Text Solution

    |

  20. If f(x) is a polynomial function of second degree. IF f(1) = f(-1) and...

    Text Solution

    |