Home
Class 12
MATHS
Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2)...

Let `P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, delta` are the roots of the equation `x ^(4) -x ^(3)-x ^(2) -1=0,` then `P (alpha ) + P (beta) +P (gamma) + P(delta)=`

Text Solution

Verified by Experts

The correct Answer is:
6
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|3 Videos

  • PROBABILITY

    VK JAISWAL ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

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

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

If alpha , beta , gamma are the roots of the equation x^3 -6x^2 +11 x +6=0 then sum alpha^2 beta =

If alpha, beta and gamma are three ral roots of the equatin x ^(3) -6x ^(2)+5x-1 =0, then the value of alpha ^(4) + beta ^(4) + gamma ^(4) is:

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

If alpha, beta , gamma, delta are the roots of the equation x^4+x^2+1=0 then the equation whose roots are alpha^2, beta^2, gamma^2, delta^2 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, beta, gamma, delta be the real of the equation x^4+4x^3-6x^2+7x-9=0 show that (1+alpha^2)(1+beta^2) (1+gamma^2)(1+delta^2) equal to 13.

Let alpha , beta, gamma, delta are roots of x ^(4) -12x ^(3) +lamda x ^(2) -54 x+ 14 =0 If alpha + beta =gamma + delta, then

VK JAISWAL ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The least rositive integral value of 'x' satisfying (e ^(x) -2) (sin (...

    Text Solution

    |

  2. The integral values of x for which x^2 +17x+71 is perfect square of a ...

    Text Solution

    |

  3. Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, de...

    Text Solution

    |

  4. The number of real values of 'a' for which the largest value of the fu...

    Text Solution

    |

  5. The number of all values of n, (whre pi is a whole number ) for which ...

    Text Solution

    |

  6. The number of negative intergral values of m for which the expression ...

    Text Solution

    |

  7. If the expression ax ^(4)+bx^(3)-x ^(2)+2x+3 has the remainder 4x +3 w...

    Text Solution

    |

  8. The smallest value of k for which both roots of the equation x^(2)-8kx...

    Text Solution

    |

  9. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  10. The sum of all real values of k for which the expression x ^(2)+2xy +k...

    Text Solution

    |

  11. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

    Text Solution

    |

  12. Find the number of integral vaues of 'a' for which the range of functi...

    Text Solution

    |

  13. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

    Text Solution

    |

  14. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  15. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

    Text Solution

    |

  16. Let p (x) be a polynomial with real coefficient and p (x)-p'(x) =x^(2)...

    Text Solution

    |

  17. Find the smallest positive integral value of a for which the greater r...

    Text Solution

    |

  18. If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real root...

    Text Solution

    |

  19. Let a,b,c, d be the roots of x ^(4) -x ^(3)-x ^(2) -1=0. Also consider...

    Text Solution

    |

  20. The number of integral value of a,a, in [-5, 5] for which the equation...

    Text Solution

    |