Home
Class 12
MATHS
Consider the equation log2 ^2 x- x - 4 l...

Consider the equation `log_2 ^2 x- x - 4 log_2 x- m^2 -2m-13=0,mepsilon 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)`

A

`(-oo, 0) `

B

`(0,oo)`

C

`[1,oo)`

D

`(-oo,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|3 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|44 Videos

  • PROBABILITY

    VK JAISWAL|Exercise Exercise -5 : Subjective Type problems|12 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

Consider the equation log_(2)^(2)x-x-4log_(2)x-m^(2)-2m-13=0,m varepsilon R Let the real roots of the equation be x_(1),x_(2), such that x_(1)

Consider the equation (log_2 x)^(2) -4 log_2 x - m^(2) - 2m -13=0 , m in R . Let the real roots 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 :

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 :

The value of m for which the equation x^(2)-x+m^(2)=0 has no real roots is given as

The exhaustive values of x for which f(x) = tan^-1 x - x is decreasing is (i) (1,infty) (ii) (-1,infty) (iii) (-infty,infty) (iv) (0,infty)

Is there any real value of 'a' for which the equation x^(2)+2x+(a^(2)+1)=0 has real roots?

Determine the value(s) of m for which the equation x^(2)+m(4x+m-1)+2=0 has real roots.

The domain of f(x)=log_x 12 is (i) (0,infty) (ii ) (0,1)cup (1,infty) (iii) (-infty,0) (iv) (2,12)

The solution set of the inequation ||x|-1| < | 1 – x|, x in RR, is (i)(-1,1) (ii)(0,infty) (iii)(-1,infty) (iv) none of these

Complete set of real values of 'a' for which the equation x^(4)-2ax^(2)+x+a^(2)-a=0 has all its roots real

VK JAISWAL-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 in R, (b,c, in R) attains its least val...

    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- x - 4 log2 x- m^2 -2m-13=0,mepsilon R...

    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) + 4x -1=0 has four distinct real roots x ...

    Text Solution

    |

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

    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 quadratic polynomical with real coefficient such tht for a...

    Text Solution

    |

  15. Let P(x) be quadratic polynomical with real coefficient such tht for a...

    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 real number satifying 2t ^(3) -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

    |