Home
Class 12
MATHS
If alpha ,beta and gamma are the roots o...

If `alpha ,beta and gamma` are the roots of
`x^3-2x^2+3x-4 =0 `, then find
(i) `sumalpha^2beta^2 (ii)sumalpha beta(alpha+beta)`

Text Solution

Verified by Experts

Since `alpha , beta, gamma ` are the roots of
`x^3-2x^2+3x-4 =0 then alpha +beta+gamma=2`
`alpha beta +betagamma+gamma alpha=3`
`alphabetagamma=4 `
(i) `sum alpha^2beta^2=alpha^2beta^2+beta^2gamma^2+gamma^2alpha^2`
`=( alpha beta +betagamma+gammaalpha)^2 -2alphabeta gamma(alpha+beta+gamma)`
=9-2.2.4=9-16=-7
(ii) `sumalphabeta(alpha+beta)=alpha^2beta+beta^2gamma+gamma^2alpha+alphabeta^2+betagamma^2+gamma alpha^2`
`=(alphabeta +betagamma+gamma alpha)(alpha+beta+gamma)-3alphabetagamma`
= 2.3-3.4=6-12=-6
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE -4(b)|24 Videos

  • THEORY OF EQUATIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE -4(c)|17 Videos

  • THEORY OF EQUATIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise DAM SURE LAQ -7 MARKS|4 Videos

  • SYSTEM OF CIRCLE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERXCISE - 2(b)|23 Videos

Similar Questions

Explore conceptually related problems

Let , alpha ,beta,gamma be the roots of x^3+px^2+qx+r=0 . Then find the (i) sumalpha^2

If alpha, beta and 1 are the roots of x^3-2x^2-5x+6=0 , then find alpha and beta

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

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

If alpha , beta , gamma are the roots of the equation x^3 +4x^2 -5x +3=0 then sum (1)/( alpha^2 beta^2)=

Let alpha ,beta, gamma be the roots of x^3+px^2+qx+r=0 then find sumalpha^3

If alpha , beta , gamma are the roots of 2x^3 -2x -1=0 the sum ( alpha beta)^2 =

If alpha, beta and gamma are the roots of x^3 +px^2+qx+r=0 then find the following : (i) alpha + beta + gamma (ii) alpha xx beta + beta xx gamma + gamma xx alpha (iii) alpha xx beta xx gamma

If alpha , beta , gamma are the roots of x^3 +2x^2 +3x +8=0 then (3-alpha )(3 - beta) (3-gamma) =

If alpha, beta, gamma are roots of x^(3) - 2x^(2) + 3x - 4 = 0 , then sum a^(2) beta^(2) =

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-THEORY OF EQUATIONS -EXERCISE -4(a)
  1. Form polynomial equations of the lowest degree , with roots as given ...

    Text Solution

    |

  2. Form polynomial equations of the lowest degree , with roots as given ...

    Text Solution

    |

  3. Form polynomial equations of the lowest degree , with roots as given ...

    Text Solution

    |

  4. If alpha,beta,gamma are the roots of 4x^3-6x^2+7x+3=0 then find th...

    Text Solution

    |

  5. if 1,1,alpha are the roots of x^3-xx^2+9x-4=0 ,then find alpha .

    Text Solution

    |

  6. If -1,2 and alpha are the roots of 2x^3 +x^2-7x-6=0 , then find alp...

    Text Solution

    |

  7. If 1,-2 and 3 are roots of x^3-2x^2+ax+6=0 , then find a .

    Text Solution

    |

  8. If the product of the roots of 4x^3+16x^2-9xa=0 is 9 , then find a .

    Text Solution

    |

  9. Find the values of s1, s2,s3 and s4 for each of the following equation...

    Text Solution

    |

  10. Find the values of s1, s2,s3 and s4 for each of the following equation...

    Text Solution

    |

  11. If alpha, beta and 1 are the roots of x^3-2x^2-5x+6=0 , then find alp...

    Text Solution

    |

  12. If alpha ,beta and gamma are the roots of x^3-2x^2+3x-4 =0 , then fi...

    Text Solution

    |

  13. If alpha, beta and gamma are the roots of x^3 +px^2+qx+r=0 then find t...

    Text Solution

    |

  14. If alpha, beta and gamma are the roots of x^3 +px^2+qx+r=0 then find t...

    Text Solution

    |

  15. If alpha, beta and gamma are the roots of x^3 +px^2+qx+r=0 then find t...

    Text Solution

    |

  16. If alpha, beta and gamma are the roots of x^3 +px^2+qx+r=0 then find t...

    Text Solution

    |

  17. If alpha, beta and gamma are the roots of x^3 +px^2+qx+r=0 then find t...

    Text Solution

    |

  18. If alpha, beta,gamma are the roots of x^3-6x^2+11x-6=0 then find t...

    Text Solution

    |

  19. If alpha ,beta,gamma are the roots of x^3 -7x +6=0 then find the eq...

    Text Solution

    |

  20. If alpha ,beta, gamma are the roots of x^3-3ax+b=0 prove that sum ...

    Text Solution

    |