Home
Class 12
MATHS
If alpha,beta,gamma are different from 1...

If `alpha,beta,gamma` are different from 1 and are the roots of `a x^3+b x^2+c x+d=0a n d(beta-gamma)(gamma-alpha)(alpha-beta)=(25)/2` , then prove that `|alpha/(1-alpha)beta/(1-beta)gamma/(1-gamma)alphabetagammaalpha^2beta^2gamma^2|=(25 d)/(2(a+b+c+d))`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

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

If alpha,beta,gamma are the roots of a x^3+b x^2+c x+d=0a n d|alpha beta gamma beta gamma alpha gamma alpha beta|=0,alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha,a n dgamma+alpha-betadot

If alpha, beta, gamma are the roots of the equation x^3 - 3x + 11 =0 , then alpha + beta + gamma is ………….

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If alpha, beta, gamma are the roots of 9x^3 - 7x + 6 = 0 , then alpha beta gamma is …………

Prove that sum_(alpha+beta+gamma = 10) (10 !)/(alpha!beta!gamma!)=3^(10)dot

If alpha, beta and gamma are the zeros of x^3 + px^2 + qx + r , then Sigma(1)/(alpha) 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,beta,gamma are the roots of the equation x^3+4x+1=0, then find the value of (alpha+beta)^(-1)+(beta+gamma)^(-1)+(gamma+alpha)^(-1) .

CENGAGE-DETERMINANTS-All Questions
  1. Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c...

    Text Solution

    |

  2. If (x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x| show...

    Text Solution

    |

  3. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

    Text Solution

    |

  4. If p+q+r=0=a+b+c =0, then the value of the determnalnt |p a q b r c q ...

    Text Solution

    |

  5. Let =|2a1b1a1b2+a2b1a1b3+a3b1a1b2+a2b1 2a2b2a2b3+a3b2a1b3+a3b1a3b2+a2b...

    Text Solution

    |

  6. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

    Text Solution

    |

  7. Evaluate |^x C1^x C2^x C3^y C1^y C2^y C3^z C1^z C2^z C3|

    Text Solution

    |

  8. Using factor theorem, show that |(-2a,a+b,c+a),(a+b,-2a,b+c),(c+a,c+b,...

    Text Solution

    |

  9. If a determinant of order 3xx3 is formed by using the numbers 1 or -1 ...

    Text Solution

    |

  10. If z=|-5 3+4i5-7i3-4i6 8+7i5+7i8-7i9|,t h e nz is purely real purely ...

    Text Solution

    |

  11. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

    Text Solution

    |

  12. If omega = cis (2pi)/(3), then number of distinct roots of |(z+1,omega...

    Text Solution

    |

  13. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

    Text Solution

    |

  14. Consider the determinant "Delta"=|a1+b1x^2a1x^2+b1c1a2+b2x^2a2x^2+b2c2...

    Text Solution

    |

  15. Evaluate : int dx/(2x^2+x+3)

    Text Solution

    |

  16. If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...

    Text Solution

    |

  17. If A , B ,a n dC are the angles of triangle, show that the system o...

    Text Solution

    |

  18. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

    Text Solution

    |

  19. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|a1a2a3 4 5a6a7a8a9|...

    Text Solution

    |

  20. Column I, Column II The value of the determinant |x+2x+3x+5x+4x+6x...

    Text Solution

    |