Home
Class 12
MATHS
Consider the cubic equation in x , x ^(3...

Consider the cubic equation in `x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0` whose roots are `alpha, beta , gamma. `
Number of value of `theta` in `[0,2pi]` for which at least two roots are equal, is :

A

2

B

3

C

4

D

5

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 cubic equation x^(3)-x^(2)+(x-x^(2))sin theta+(x-x^(2))cos theta+(x-1)sin theta cos theta=0 Whose roots are alpha,beta,gamma then

Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0 whose roots are alpha, beta , gamma. The value of ((alpha)/(2))^(2) + ((beta)/(2 )) ^(2) + ((gamma)/(2 ))^(2) =

Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta+cos theta+sin theta)x-sin theta*cos theta=0 Whose roots are x_(1),x_(2) and x_(3)

8sin theta cos theta cos2 theta cos4 theta=sin x rArr x=

(sin3 theta-sin theta * sin ^ (2) (2 theta)) / (sin theta + sin2 theta * cos theta) = cos x rarr x =

8sin theta cos theta cos2 theta cos4 theta=sin x the x=

8sin theta cos theta*cos2 theta cos4 theta=sin x rArr x=

If -pi (cos 3 theta + 1)x^(2) + 2(cos 2theta - 1)x +(1 - 2 cos theta) = 0 has more than two roots for

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

    |