Home
Class 12
MATHS
Let t be a real number satifying 2t ^(3)...

Let t be a real number satifying `2t ^(3) -9t ^(2) + 30 -lamda =0` where `t =x + 1/xand lamda in R.`
if the cubic has exactly two real and distinct solutions for x then exhaustive set of values of `lamda` be:

A

`lamda in (-oo, 3) uu (30, oo)`

B

`lamda in (-oo, -22) uu (10, oo) uu {3}`

C

`lamda in {3,30}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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

Let t be a real number satifying 2t ^(3) -9t ^(2) + 30 -lamda =0 where t =x + 1/xand lamda in R. If the above cubic has three real and distinct solutions for x then exhaustive set of value of lamda be :

In a DeltaABC ,angleB=(2pi)/3 and cos A + cos c = lamda . Then , the exhaustive set of value of lamda is

If t is a real number satisfying the equation 2t^(3)-9t^(2)+30-a=0, then find the values of the parameter a for which the equation x+(1)/(x)=t gives six real and distinct values of x .

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

If f (x)= tan ^(-1) (sgn (n ^(2) -lamda x+1)) has exactly one point of discontinuity, then the value of lamda can be:

y=3cos 100pi(2t-x) , the value of lamda is

Let alpha, beta be two real roots of the equation cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R . If cot ( alpha + beta ) = (1)/(2) , then value of lamda is :

If the system of equation r^(2)+s^(2)=t and r+s+t=(k-3)/(2) has exactly one real solution, then the value of k is

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

    |