Home
Class 12
MATHS
If alpha, beta (alpha lt beta) are the r...

If `alpha, beta (alpha lt beta)` are the real roots of the equation `x ^(2)-(k +4) x+ k ^(2)-12=0` such that `4 in (alpha, beta)` , then the number of integral values of k equal to :

A

4

B

5

C

6

D

7

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 (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|42 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|23 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

If alpha,beta(alpha lt beta) are the real roots of equation x^2-(k+4)x+k^2-12=0 such theta 4 in (alpha,beta) , then the number of integral value of k is equal to

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then

If alpha and beta are the roots of the equation x^(2)+alpha x+beta=0 such that alpha ne beta , then the number of integral values of x satisfying ||x-beta|-alpha|lt1 is

If alpha, beta (alpha lt beta) are the roots of the equation 6x^(2) + 11x + 3 = 0 , then which of the following are real ?

If alpha and beta are the roots of the equation x^(2)-px +16=0 , such that alpha^(2)+beta^(2)=9 , then the value of p is

If alpha, beta be the roots of 4x^(8) - 16x + c = 0, c in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 , then the number of integral values of c is

If alpha and beta are the roots of the equation 2x^(2) - 3x + 4 = 0 , then alpha^(2) + beta^(2) = ____

If alpha and beta are the root of the equation x^(2) - 4x + 5 = 0 , then alpha^(2) + beta^(2) = ________

If alpha and beta are the roots of the quadratic equation x^(2) - 4x - 6 = 0 , find the values of alpha^(2) + beta^(2) .

If alpha, beta are the roots of the equation x^(2)+alphax + beta = 0 such that alpha ne beta and ||x-beta|-alpha|| lt alpha , then

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If alpha, beta (alpha lt beta) are the real roots of the equation x ^(...

    Text Solution

    |

  2. Let f (x) =ax ^(2) + bx+ c where a,b,c are integers. If sin ""pi/7. si...

    Text Solution

    |

  3. Let a, b, c, d be distinct integers such that the equation (x - a) (x ...

    Text Solution

    |

  4. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1), w...

    Text Solution

    |

  5. The number of positive integral values of , m le 16 for which the equa...

    Text Solution

    |

  6. If the equation (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then...

    Text Solution

    |

  7. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

    Text Solution

    |

  8. The integral values of x for which x ^(2) + 17 x +7 is perfect square ...

    Text Solution

    |

  9. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

    Text Solution

    |

  10. The number of real values of 'a' for which the largest value of the fu...

    Text Solution

    |

  11. The number of all values of n, (whre n is a whole number ) for which t...

    Text Solution

    |

  12. The number of negative intergral values of m for which the expression ...

    Text Solution

    |

  13. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

    Text Solution

    |

  14. The smallest value of k for which both roots of the equation x^(2)-8kx...

    Text Solution

    |

  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

    Text Solution

    |

  17. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

    Text Solution

    |

  18. Find the number of integral vaues of 'a' for which the range of functi...

    Text Solution

    |

  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

    Text Solution

    |

  20. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  21. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

    Text Solution

    |