Home
Class 12
MATHS
If alpha, beta, gamma are roots of the e...

If `alpha, beta, gamma` are roots of the equation `x^3+x^2+2 x-4=0`, then value of `|[1+alpha, 1, 1],[ 1, 4-beta^3 , 1 ],[ 1 , 1, 4-gamma^3]|` (where `alpha` is real)

Text Solution

Verified by Experts

The correct Answer is:
40
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    CENGAGE|Exercise Question Bank|23 Videos

  • 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 roots of the equation "x^(3)+x^(2)+2x-4=0," then value of "|[4-alpha,1,1],[1,4-beta,1],[1,1,4-gamma]|" (where "alpha" is real) "

If alpha, beta, gamma are roots of equation x^(3)-x-1=0 then the value of sum(1+alpha)/(1-alpha) is :

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

If alpha,beta,gamma are the roots of the equation (x^3+x^2+x+1)=0 then |{:(1+alpha^2," "1," "1),(" "1,1+beta^2," "1),(" "1," "1,1+gamma^2):}| is equal to

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

If alpha,beta,gamma are the roots of the equation (x^3+x^2+x+1)=0 then |{:(1+alpha," "1," "1),(" "1,1+beta," "1),(" "1," "1,1+gamma):}| is equal to

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

CENGAGE-DETERMINANTS-Question Bank
  1. If the equations p x+2 y-3=0, x+3 y-4=0 and p x^2+3 y^2+3 x y+(q-3) x-...

    Text Solution

    |

  2. Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x...

    Text Solution

    |

  3. Given 2 x-y+2 z=1 , x-2 y+z=-4 , and x+y+lambda z =4. Then the. value ...

    Text Solution

    |

  4. If M and m are maximum and minimum value, respectively of |[1 , cos th...

    Text Solution

    |

  5. The value of |[log (3) 512 , log (4) 3 ],[ log (3) 8 , log (4) 9]||[...

    Text Solution

    |

  6. If x in[0, (pi)/2] such that |(sin x+cos x)-sqrt2| +|y+(1)/(y)-2|+|z| ...

    Text Solution

    |

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

    Text Solution

    |

  8. If p and q are real so that sysiem of equations p x+4 y +z=0,2 y+3 z=1...

    Text Solution

    |

  9. If |[1 , x, x^2],[ x , x^2 , 1],[ x^2 , 1 , x]|=3, then the value ...

    Text Solution

    |

  10. Let f(x) = |[x,1,(-3)/(2)],[2,2,1],[(1)/(x-1) ,0,(1)/(2)]| . The miniu...

    Text Solution

    |

  11. In the determinant, Delta=|[-2, 5 , -1],[ 4 , 7, 0],[ 5, -3, 1]|...

    Text Solution

    |

  12. If |[x^2, x^4 , (x-1)^2],[ 0, 4, 6 x^2 ],[ 4 ,1,7] |= overset(6) ...

    Text Solution

    |

  13. If a, b, c are the sides of a scalene triangle such that |[a , a^2 , a...

    Text Solution

    |

  14. Number of real roots of the equation |[sin x , x], [1 , 1]||[cos x, ...

    Text Solution

    |

  15. Let a+b+c=s and |[s+c, a, b],[ c ,s+a, b],[ c, a , s+b]|is cqua...

    Text Solution

    |

  16. In triangle A B C, if |[1, a, b],[ 1 , c, a],[ 1, b, c]|=0 then...

    Text Solution

    |

  17. If system of linear equations (a-1) x+z=alpha1 x+(b-1) y=beta and y+(c...

    Text Solution

    |

  18. If a1, a2, a3, 5,4, a6, a7, a8, a9 are in H . P, then the value of the...

    Text Solution

    |

  19. If 0 le[x]lt 2,-1 le[y] lt 1 and 1 le[z] lt 3 where [.] denotes greate...

    Text Solution

    |

  20. If f(x)=tan x and A, B, C are the angles of triangle A B C, then |[f(A...

    Text Solution

    |