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)=`

A

`4`

B

`6`

C

`8`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `P(x)=x^(6)-x^(5)-x^(3)-x^(2)-x` and `Q(x)=x^(4)-x^(3)-x^(2)-1`
Here` P(x)=Q(x)(x^(2)+1)+x^(2)-x+1`
`:. sumP(alpha)=sumalpha^(2)-sumalpha+4`
`=(sumalpha)^(2)-2sum(alphabeta)-sumalpha+4`
`=1-2(-1)-(1)+4`
`=6`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION|121 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 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 and gamma, delta are the roots of the equations x^2-bx+c=0 and x^2-px+q=0 respectively, show that , (alpha-gamma)(beta-delta) -alpha.gamma - beta. delta=(c+q)-bp .

If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^2+7x-9=0, then the value of (1+alpha^2)(1-beta^2)(1-gamma^2)(1-sigma^2) is a. -75 b. 25 c. 0 d. 75

IF alpha and beta are the roots of the equation x(x-3)=4, find the value of alpha^2+beta^2 .

IF alpha,beta and gamma,delta be the roots of the equation x^2+px-r=0 and x^2+px+r=0 respectively, prove that (alpha-gamma)(alpha-delta)=(beta-gamma)(beta-delta)

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

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

If alpha , beta , gamma are the roots of the equation 9x^(3)-7x+6=0 then the equation x^(3)+Ax^(2)+Bx+C=0 has roots 3alpha+2 , 3beta+2 , 3gamma+2 , where

IF the roots of the equation 3x^2+8x+2=0 are alpha,beta then (1/alpha+1/beta) =

CENGAGE PUBLICATION-THEORY OF EQUATIONS-Single correct Answer
  1. The difference of maximum and minimum value of (x^(2)+4x+9)/(x^(2)+9) ...

    Text Solution

    |

  2. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  3. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

    Text Solution

    |

  4. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  5. The equation ax^(4)-2x^(2)-(a-1)=0 will have real and unequal roots if

    Text Solution

    |

  6. If ax^(2)+bx+c=0, a ne 0, a, b, c in R has distinct real roots in (1,2...

    Text Solution

    |

  7. If c lt a lt b lt d, then roots of the equation bx^(2)+(1-b(c+d)x+bcd-...

    Text Solution

    |

  8. If 2a, b, 2c are in A.P. where a, b, c are R^(+), then the expression ...

    Text Solution

    |

  9. If a, b, c are positive numbers such that a gt b gt c and the equation...

    Text Solution

    |

  10. If the quadratic equation x^(2)-36x+lambda=0 has roots alpha and beta ...

    Text Solution

    |

  11. If the equation 2^(2x)+a*2^(x+1)+a+1=0 has roots of opposite sign, the...

    Text Solution

    |

  12. Let a, b, c ne three distinct non-zero real numbers satisfying the sys...

    Text Solution

    |

  13. In the given figure graph of y=p(x)=x^(4)+ax^(3)+bx^(2)+cx+d is given ...

    Text Solution

    |

  14. If a^(3)-3a^(2)+5a-17=0 and b^(3)-3b^(2)+5b+11=0 are such that a+b is ...

    Text Solution

    |

  15. Let f(x) = x^4 + ax^3 + bx^2 + cx + d be a polynomial with real coeffi...

    Text Solution

    |

  16. If f(x) is a polynomial of degree four with leading coefficient one s...

    Text Solution

    |

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

    Text Solution

    |

  18. The line y=mx+1 touches the curves y=-x^(4)+2x^(2)+x at two points P(x...

    Text Solution

    |

  19. If a+2b+3c=4, then find the least value of a^2+b^2+c^2dot

    Text Solution

    |

  20. If the roots of x^(4)+qx^(2)+kx+225=0 are in arthmetic progression, th...

    Text Solution

    |