Home
Class 12
MATHS
The coefficient of the quadratic equatio...

The coefficient of the quadratic equation `a x^2+(a+d)x+(a+2d)=0` are consecutive terms of a positively valued, increasing arithmetic sequence. Then the least integral value of `d//a` such that the equation has real solutions is __________.

Text Solution

Verified by Experts

The correct Answer is:
`3059`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

The number of integral values of n such that the equation 2n{x}=3x+2[x]has exactly 5 solutions.

The quadratic equation 2x^(2) + x + 4 has ………real roots

Find the least positive value of k for which the equation x^(2)+kx+4=0 has real roots.

If the roots of the quadratic equation x^(2)-4x-log_(3)a=0 are real,then the least value of a is

If the roots of the quadratic equation x^(2)-2kx+2k^(2)-4=0 are real,then the range of the values of k is

The least +ve integral value of 'a' for which the equation 3x^4 +4x^3-12x^2 +5a=0 has no real root is

RESONANCE-DPP-QUESTION
  1. If the sum of n term of the series (5)/(1.2.3) + (6)/(2.3.4) + ( 7)/(3...

    Text Solution

    |

  2. If the 8th term of an A.P. is 31 and the 15th term is 16 more than ...

    Text Solution

    |

  3. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

    Text Solution

    |

  4. Let f(r) = sum(j=2)^(2008) (1)/(j^(r)) = (1)/(2^(r))+(1)/(3^(r))+"…."+...

    Text Solution

    |

  5. If sinalphacosbeta = (-1)/(2), then find the range of value of cosalph...

    Text Solution

    |

  6. -cos(A+B)cos(B-A) =

    Text Solution

    |

  7. Find the value of xsqrt(6x^(4) + 4x^(2) + 2) gt -2x^(2) + 5x - 4

    Text Solution

    |

  8. S = n xx 10^(6m) + n xx 10^(6m - 1) + n xx 10^(6m-2)+ "…." + nxx 10 + ...

    Text Solution

    |

  9. Number of roots of (x^(2)+5x+7)(-x^(2)+3x-4) = 0

    Text Solution

    |

  10. If the roots of Quadratic i^(2)x^(2)+5ix-6 are a+ib and c +id (a,b,c,d...

    Text Solution

    |

  11. S(10) = cos'(pi)/(180) + cos'(3pi)/(180) + "….." cos '(19pi)/(180)

    Text Solution

    |

  12. Find the sum of the series 31^(3) + 32^(3) + "……." 50^(3)

    Text Solution

    |

  13. Find maximum value of a^(2)b^(3) if a+b=2. When a & b are positive num...

    Text Solution

    |

  14. Find the roots of the equation x^(2) + ix - 1 - i = 0

    Text Solution

    |

  15. solve ||x-2|-1|lt 2

    Text Solution

    |

  16. If x^(3) + 2x-3 = 0 then then number of real values of 'x' satisfying ...

    Text Solution

    |

  17. solve for x |x+1| + |x-2| + |x-5| = 4

    Text Solution

    |

  18. If |a-b| gt ||a|-|b|| then

    Text Solution

    |

  19. The inequation sqrt(f(x)) gt g(x), is equivalent to the

    Text Solution

    |

  20. The value of sintheta + sin3theta +sin5theta + "….."+ sin(2n-1)theta i...

    Text Solution

    |