Home
Class 12
MATHS
Let alpha+ibeta;alpha,beta in R , be a ...

Let `alpha+ibeta;alpha,beta in R ,` be a root of the equation `x^3+q x+r=0; q ,r in Rdot` A real cubic equation, independent of `alpha&beta,` whose one root is `2alpha` is (a)`x^3+q x-r=0` (b) `x^3-q x+4=0` (c)`x^3+2q x+r=0` (d) None of these

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

If alpha and beta are the roots of the equation 2x^(2)+3x+2=0 , find the equation whose roots are alpha+1 and beta+1 .

If alpha, beta be the roots of the equation x^2-px+q=0 then find the equation whose roots are q/(p-alpha) and q/(p-beta)

If alpha,beta are the roots of the equation x^(2)+x+1=0 , find the value of alpha^(3)-beta^(3) .

If alpha , beta , gamma are the roots of the equation x^3 +px^2 +qx +r=0 then sum alpha^2 ( beta + gamma)=

If alpha, beta are roots of the equation x^(2) + x + 1 = 0 , then the equation whose roots are (alpha)/(beta) and (beta)/(alpha) , is

If alpha, beta, gamma, are the roots of the equation x^(3)+3x-1=0, then equation whose roots are alpha^(2),beta^(2),gamma^(2) is

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta is :

Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != 0 .If p,q,r are in A.P. and 1/alpha+1/beta=4 , then the value of |alpha-beta| is :

Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != 0 .If p,q,r are in A.P. and 1/alpha+1/beta=4 , then the value of |alpha-beta| is :

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. A shopkeeper places before you 41 different toys out of which 20 toys ...

    Text Solution

    |

  2. If the solution of the differential equation (dy)/(dx)=1/(xcosy+sin2y)...

    Text Solution

    |

  3. Let alpha+ibeta;alpha,beta in R , be a root of the equation x^3+q x+r...

    Text Solution

    |

  4. In triangle ABC, right-angled at B. if tanA=1/(sqrt(3)) find the...

    Text Solution

    |

  5. The curve which passes through (1, 2) and whose sub-normal at every ...

    Text Solution

    |

  6. The function f(x)=int(-1)^x t(e^t-1)(t-1)(t-2)^3(t-3)^5dt has a local ...

    Text Solution

    |

  7. A bag contains 50 tickets numbered 1, 2, 3, .., 50 of which five are d...

    Text Solution

    |

  8. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

    Text Solution

    |

  9. If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)...

    Text Solution

    |

  10. Area bounded by the curve y=maxdot{(sin x ,cos x)} and x -axis, betwee...

    Text Solution

    |

  11. If 1lt=rlt=n , then \ n^(n-1)Cr 1 =(n-r+1)\ ^n C(r-1)dot

    Text Solution

    |

  12. The length of the transverse axis of the hyperbola 9x^(2)-16y^(2)-18x ...

    Text Solution

    |

  13. Value of the parameter ' a ' such that the area bounded by y=a^2x^2+a...

    Text Solution

    |

  14. The line y=m x bisects the area enclosed by the curve y=1+4x-x^2 and t...

    Text Solution

    |

  15. The chord of contact of the pair of tangents drawn from each point on ...

    Text Solution

    |

  16. The extremities of a diagonal of a rectangle are (0,0) and (4,3). The ...

    Text Solution

    |

  17. If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 repr...

    Text Solution

    |

  18. If x(1),x(2)& x(3) are three distinct numbers which satisfy the ralati...

    Text Solution

    |

  19. The area (in sq. units) of the quadrilateral formed by the tangents ...

    Text Solution

    |

  20. The value of int (sin x cos x)/(sqrt(1-sin^(4)x)) dx is equal to :

    Text Solution

    |