Home
Class 12
MATHS
Consider the equation log (2)^(2) x -4 l...

Consider the equation `log _(2)^(2) x -4 log _(2)x-m^(2) -2m -13=0, m in R.` Let the real roots of the equation be `x _(1), x _(2)` such that `x _(1)lt x _(2).`
The sum of maximum value of, `x _(1)` and minimum value of `x _(2)` is :

A

`(513)/(8)`

B

`(513)/(4 )`

C

`(1025)/(8)`

D

`(257)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|4 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|42 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

Solve the equation: log_(2x+3)x^(2) lt log_(2x)(2x+3)

Consider the equation log_2 ^2 x- 4 log_2 x- m^2 -2m-13=0,m in R. Let the real roots of the equation be x_1,x_2, such that x_1 < x_2 .The set of all values of m for which the equation has real roots is (i) (-infty ,0) (ii) (0,infty) (iii) [1, infty) (iv) (-infty,infty)

Solve the equation log_4 (2x^2 + x + 1) - log_2 (2x - 1) = 1.

Let x_1 and x_2 be the real roots of the equation x^(2) -kx +(k^(2) +7x+15)=0 if the maximum value of (x_1^(2) + x_2^(2)) is (18)/(x) , then find the value of x .

If the minimum value of x^2+2x+3 is m and maximum value of -x^2+4x+6 is M then m+M=

If x_1 and x_2 are the solutions of the equation x^(log_(10)x)=100x such that x_1gt1 and x_2lt1 , the value of (x_1x_2)/2 is

Let x_1 and x_2 be the real roots of the equation x^2 -(k-2)x+(k^2 +3k+5)=0 then the maximum value of x_1^2+x_2^2 is

The number of roots of the equation 1+log_(2)(1-x)=2^(-x) , is

The solution of the equation log _( cosx ^(2)) (3-2x) lt log _( cos x ^(2)) (2x -1) is:

The number of real roots of the equation log_(1//3)(1+sqrt(x))+log_(1//3)(1+x)=2 , is

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. If alpha, beta the roots of equation (k + 1 )x ^(2) -(20k +14) x + 91...

    Text Solution

    |

  2. Let f (x) =x ^(2) + bx + c AA xin R, (b,c, in R) attains its least va...

    Text Solution

    |

  3. Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least val...

    Text Solution

    |

  4. Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least val...

    Text Solution

    |

  5. Consider the equation log2 ^2 x- 4 log2 x- m^2 -2m-13=0,m in R.Let the...

    Text Solution

    |

  6. Consider the equation log (2)^(2) x -4 log (2)x-m^(2) -2m -13=0, m in ...

    Text Solution

    |

  7. The equation x ^(4) -2x ^(3)-3x^2 + 4x -1=0 has four distinct real roo...

    Text Solution

    |

  8. The equation x ^(4) -2x ^(3)-3x^2 + 4x -1=0 has four distinct real roo...

    Text Solution

    |

  9. Let f(x) polynomial of degree 5 with leading coefficient unity such th...

    Text Solution

    |

  10. Let f (x) be a polynomial of degree 5 with leading coefficient unity,...

    Text Solution

    |

  11. Let f (x) be a polynomial of degree 5 with leading coefficient unity,...

    Text Solution

    |

  12. Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin th...

    Text Solution

    |

  13. Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin th...

    Text Solution

    |

  14. Let P (x ) be a quadratic polynomial with real coefficients such that...

    Text Solution

    |

  15. Let P (x ) be a quadratic polynomial with real coefficients such that...

    Text Solution

    |

  16. Let t be a ral number satifying 2t ^(2) -9t ^(2) + 30 -lamda =0 where ...

    Text Solution

    |

  17. Let t be a ral number satifying 2t ^(2) -9t ^(2) + 30 -lamda =0 where ...

    Text Solution

    |

  18. Let t be a ral number satifying 2t ^(2) -9t ^(2) + 30 -lamda =0 where ...

    Text Solution

    |

  19. Consider a quadratic expression f (x) =tx^(2) -(2t -1) x+ (5x -1) If...

    Text Solution

    |

  20. Consider a quadratic expression f (x) =tx^(2) -(2t -1) x+ (5x -1) I...

    Text Solution

    |