Home
Class 12
MATHS
If alpha, beta and gamma are the cubic e...

If `alpha, beta and gamma` are the cubic equation `x^3-6x^2+11x-6=0`. From a cubic equation whose roots are `2alpha, 2beta, 2gamma`.

Text Solution

Verified by Experts

The correct Answer is:
`x^3-12x^2+44x-48=0`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    FULL MARKS|Exercise EXERCISE 3.7|10 Videos

  • SAMPLE PAPER-09 (UNSOLVED)

    FULL MARKS|Exercise PART-IV (IV. Answer all the questions. )|15 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY-II

    FULL MARKS|Exercise Additional Question Solved|44 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^2 + 3x + 4 = 0, for a cubic equation roots are 2 alpha, 2 beta, 2 gamma

If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^2 + 3x + 4 = 0, for a cubic equation roots are -alpha, -beta, -gamma

If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^2 + 3x + 4 = 0, for a cubic equation roots are 1/alpha, 1/beta, 1/gamma

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

If alpha , beta, gamma are the roots of the equation x^3-4x^2+3x-1=0 , then the equation whose roots are (alpha+beta+gamma), alphabetagamma is :

If alpha,beta,gamma are the roots of the equation x^3-p x+q=0, then find the cubic equation whose roots are alpha/(1+alpha),beta/(1+beta),gamma/(1+gamma) .

If alpha and beta are the roots of the equation 3x^(2)-6x+1=0 form the equation whose roots are 2alpha + beta and 2beta + alpha

If alpha and beta are the roots of the equation 3x^(2) - 4x+1=0 form a quadratic equation whose roots are (alpha^2)/(beta) and beta^(2)alpha .

FULL MARKS-THEORY OF EQUATIONS -Additional Questions Solved
  1. Construct a cubic equation with roots 2,3,4.

    Text Solution

    |

  2. If alpha, beta and gamma are the cubic equation x^3-6x^2+11x-6=0. From...

    Text Solution

    |

  3. If the roots of x^4+5x^3-30x^2-40x+64=0 are in G. P , then find the ro...

    Text Solution

    |

  4. Determine the value of k such that the equation (2k-5)x^2-4x-15=0 and ...

    Text Solution

    |

  5. If alpha, beta , gamma are the roots of the equation x^3+px^2+qx+r=0 ....

    Text Solution

    |

  6. alpha , beta , gamma are the roots of the equation x^3+3x^2+2x+1=0 . F...

    Text Solution

    |

  7. Find a polynomial equation of minimum degree with rational coefficient...

    Text Solution

    |

  8. Find a polynomial equation of minimum degree with rational co - effici...

    Text Solution

    |

  9. If the roots of equation x^3+px^2+qx+r=0 are in A.P then show that 2p...

    Text Solution

    |

  10. Solve 27x^3+42x^2-28x-8=0 given that its roots are in geometric progre...

    Text Solution

    |

  11. Solve the equation 15x^3-23x^2+9x-1=0 . Where roots are in H . P

    Text Solution

    |

  12. If one root of x^3+2x^2+3x+k=0 is sum of the other two roots then find...

    Text Solution

    |

  13. If sum of the roots of the equation x^3-3x^2-16x+k=0 is zero then find...

    Text Solution

    |

  14. Find all zeros of the polynomial x^3-5x^2-9x-5=0 , If 2 + I is a root.

    Text Solution

    |

  15. Solve (x-3)(x-6)(x-1)(x+2)+54=0

    Text Solution

    |

  16. Solve the equation (x-4)(x-2)(x-1)(x+1)+8=0

    Text Solution

    |

  17. Solve : 3^(2x+4)+1=2.3^(x+2)

    Text Solution

    |

  18. Solve : 2^(2x)-2^(2x+3)+2^4=0

    Text Solution

    |

  19. Solve (x-4)(x+2)(x+3)(x-3)+8=0

    Text Solution

    |

  20. Solve : (x+y)^(2//3)+2(x-y)^(2//3)=3(x^2-y^2)^(1//3) and 3x-2y=13.

    Text Solution

    |