Home
Class 12
MATHS
If a(k),(k-1,2,3,4) be the roots of the ...

If `a_(k),(k-1,2,3,4)` be the roots of the equation `px^(4)+qx+p=0`, then the equation whose roots are
`(alpha_(1)^(5))/((alpha_(2)+alpha_(3)+alpha_(4))^(2).alpha_(2)alpha_(3)alpha_(4))` is
`(alpha_(2)^(5))/((alpha_(1)+alpha_(3)+alpha_(4))^(2).alpha_(1)alpha_(3)alpha_(4))`
`(alpha_(3)^(5))/((alpha_(1)+alpha_(2)+alpha_(4))^(2).alpha_(1)alpha_(2)alpha_(4))`
`(alpha_(4)^(5))/((alpha_(1)+alpha_(2)+alpha_(3))^(2).alpha_(1)alpha_(2)alpha_(3))`

A

`p^(4)x^(4)+4p^(3)qx^(3)+6p^(2)q^(2)x^(2)`
`+(4pq^(3)-q^(4))x+q^(4)=0`

B

`q^(4)x^(4)+4p^(3)x^(3)+6p^(2)x^(2)`
`+(4q-p^(4))x+1=0`

C

`p^(4)x^(4)-4p^(3)qx^(3)+6p^(2)q^(2)x^(2)`
`-(4pq^(3)-q^(4))x+1=0`

D

`q^(4)x^(4)-4p^(3)x^(3)+6p^(2)x^(2)`
`-(4q-p^(4))x+1=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • NTA TPC JEE MAIN TEST 49

    NTA MOCK TESTS|Exercise MATHEMATICS |30 Videos

  • NTA TPC JEE MAIN TEST 51

    NTA MOCK TESTS|Exercise MATHEMATICS |30 Videos

Similar Questions

Explore conceptually related problems

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

If alpha_(2)

if sqrt(alpha_(1)-1)+2sqrt(alpha_(2)-4)+3sqrt(alpha_(3)-9)+4sqrt(alpha_(4)-16)=(alpha_(1)+alpha_(2)+alpha_(3)+alpha_(4))/(2) where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are all real. Then

If the roots of equation x^3+a x^2+b=0a r ealpha_1,alpha_2 and alpha_3(a ,b!=0) , then find the equation whose roots are (alpha_1alpha_2+alpha_2alpha_3)/(alpha_1alpha_2alpha_3),(alpha_2alpha_3+alpha_3alpha_1)/(alpha_1alpha_2alpha_3),(alpha_1alpha_3+alpha_1alpha_2)/(alpha_1alpha_2alpha_3)

If alpha is an imaginary roots of x^(5)-1=0, then the equation whose roots are alpha+alpha^(4) and alpha^(2)+alpha^(3) is

alpha=e^((2 pi)/(5)i)then1+alpha+alpha^(2)+alpha^(3)+alpha^(4)+2 alpha^(5)=

If alpha, beta are the roots of the equation x^2-bx+c=0 then find the equation whose roots are (alpha^2+beta^2)(alpha^3+beta^3) and alpha^5 beta^3+alpha^3beta^5-2alpha^4beta^4

If alpha is a root of the equation 4x^(2)+2x-1=0 then the other root is given by O -2 alpha-1 O 4 alpha^(2)+alpha-1 O 4 alpha^(3)-3 alpha O 4 alpha^(2)-3 alpha

If alpha_(1),alpha_(2),alpha_(3),.........,alpha_(n) are the roots of f(x)=0 then the equation whose roots (alpha_(1))/(K),(alpha_(2))/(K),(alpha_(3))/(K),.........(alpha_(n))/(K) is where , K!=0

If alpha_(1),,alpha_(2),...,alpha_(n) are the roots of equation x^(n)+nax-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(2))...(alpha_(1)-alpha_(n))=n(alpha_(1)^(n-1)+a)

NTA MOCK TESTS-NTA TPC JEE MAIN TEST 50-MATHEMATICS
  1. Let A =[(1,2,1),(0,1,-1),(3,-1,1)] then A^(-1) is equal to

    Text Solution

    |

  2. The sum of the series 8!+(9!)/(2!)+(10!)/(3!)+(11!)/(4!)+….. up to 2...

    Text Solution

    |

  3. If a(k),(k-1,2,3,4) be the roots of the equation px^(4)+qx+p=0, then t...

    Text Solution

    |

  4. The sum of the n terms of the series 1/2+3/4+7/8+15/16+…….is

    Text Solution

    |

  5. Consider the following statements 1. Identify , relation in a finite...

    Text Solution

    |

  6. Inside the circle S:x^(2)+y^(2)=4, there are 3 smaller circles of equa...

    Text Solution

    |

  7. The equation of tangent at the vertex of parabola x^(2)+8x+4=0 is

    Text Solution

    |

  8. Let A(-3,2) and B(-2,1) be the vertices of a DeltaABC.I f the centroid...

    Text Solution

    |

  9. The coordinates of the foot of perpendicular from the point (1,0,0) to...

    Text Solution

    |

  10. Given that veca is | to vecb and p is a non zero scalar if pvecr+(vecr...

    Text Solution

    |

  11. If f(x)=3x^(10)-7x^(8)+5x^(6)-21x^(3) then +3x^(2)-7 lim(alphato 0)(...

    Text Solution

    |

  12. The number of positive real roots of equation (x-1)(x-2)(x-3) is +...

    Text Solution

    |

  13. Let y=f(x) be a function satisfying the differential equation x (dy)/(...

    Text Solution

    |

  14. Let int(sqrt(x))/(sqrt(x^(3)+8))dx=lamda"In"|x^(3/2)+sqrt(x^(3)+8|)+C,...

    Text Solution

    |

  15. An observer on the top of a tree finds the angle of depression of a ar...

    Text Solution

    |

  16. Suppose x and y are real numbers and that x^(2)+9y^(2)-4x+6y+4=0, then...

    Text Solution

    |

  17. The value of cos(1/2cos^(-1)(cos("sin"^(-1)(sqrt(63))/8))) is

    Text Solution

    |

  18. A tangent to the hyperbola x^(2)-2y^(2)=4 meets x-axis at P and y-axis...

    Text Solution

    |

  19. A function f is defined as f(x)=(k-x^(2)+3x)/(-4+x) where k isa para...

    Text Solution

    |

  20. If lim(xto0)(tan((pi)/4+x))^(3/x)=e^(m), then the value of m is equal ...

    Text Solution

    |