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

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

    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

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

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 .

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 :

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 :

2x^2 -4x=t In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?

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

If the difference of the roots of x^(2)-lamdax+8=0 be 2 the value of lamda is

The circle x^2+y^2+4lamdax=0 which lamda in R touches the parabola y^2=8x . The value of lamda is given by

r (x) =3x -7 t (x) =3x + r (x) The function r and t are defined above. What is the value of t (2) ?

A wave is propagating on a long stretched string along its length taken as the positive x-axis. The wave equation is given as y=y_0e^(-(t/T-x/lamda)^(2)) where y_0=4mm, T=1.0s and lamda=4cm .(a) find the velocity of wave. (b) find the function f(t) giving the displacement of particle at x=0. (c) find the function g(x) giving the shape of the string at t=0.(d) plot the shape g(x) of the string at t=0 (e) Plot of the shape of the string at t=5s.

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

    |