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

`alpha` ,`beta`, `gamma` are the roots of the equation `x^(3)-3x^(2)+6x+1=0`. Then the centroid of the triangle whose vertices are `(alpha beta,1/(alpha beta))`, `(beta gamma, 1/(beta gamma))` , `(gamma alpha,1/(gamma alpha))` is

Answer

Step by step text solution for alpha ,beta, gamma are the roots of the equation x^(3)-3x^(2)+6x+1=0. Then the centroid of the triangle whose vertices are (alpha beta,1/(alpha beta)), (beta gamma, 1/(beta gamma)) , (gamma alpha,1/(gamma alpha)) is by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

If alpha, beta gamma are the real roots of the equation x^(3)-3px^(2)+3qx-1=0 , then find the centroid of the triangle whose vertices are (alpha, (1)/(alpha)), (beta, (1)/(beta)) and (gamma, (1)/(gamma)) .

If alpha,beta,gamma are the real roots of the equation x^(3)-3ax^(2)+3bx-1=0 then the centroid of the triangle with vertices (alpha,(1)/(alpha))(beta,(1)/(beta)) and (gamma,1/ gamma) is at the point

Knowledge Check

  • If alpha,beta, gamma are the real roots of the equation x^(3)-3ax^(2)+3bx-1=0 , then the centroid of the triangle whose vertices are the points (alpha, 1/(alpha)), (beta, 1/(beta)) and (gamma,1/(gamma)) is the point

    A
    `(a,b)`
    B
    `(a,-b)`
    C
    `(-a,b)`
    D
    `(-a,-b)`

  • If alpha, beta, gamma are the roots of the equation x^(3)-3x+11=0 then the equation whose roots are beta + gamma, gamma + alpha, alpha +beta is

    A
    `x^(3)+3x+11=0`
    B
    `x^(3)-3x-11=0`
    C
    `x^(3)+3x-11=0`
    D
    none

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

    A
    `x^(3)-6x^(2)+216=0`
    B
    `x^(3)-3x^(2)+112=0`
    C
    `x^(3)+6x^(2)-216=0`
    D
    `x^(3)+3x^(2)-112=0`

    • Similar Questions

    Explore conceptually related problems

    If alpha,beta,gamma are the real roots of the equation,x^(3)-3px^(2)+3qx-1=0, the centroid of the triangle whose vertices are (alpha,(1)/(alpha)),(beta,(1)/(beta)),(gamma,(1)/(gamma))quad is(p,p)(b)(p,0)(p,q)(d)(q,0)

    If alpha ,beta, gamma are roots of the cubic equation x^(3)+2x^(2)-x-3=0 then Area of the triangle with vertices (alpha,beta),(beta,gamma),(gamma,alpha) is:

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

    If alpha,beta,gamma are the roots of the equation x^(3)+qx+r=0 then find the equation whose roots are ( a )alpha+beta,beta+gamma,gamma+alpha(b)alpha beta,beta gamma,gamma alpha

    If alpha, beta, gamma are the root of the equation x^(3)-3x+11=0 then the equation whose roots are (alpha+beta), (beta-gamma) and (gamma+alpha) is :

    Home
    Profile