Let `alpha + beta +gamma` , be the real sulution of the equartion `2e^(-{x})=(x+1)` then represent fractional of x)

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

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

Let alpha, beta and gamma are the roots of the equation 2x^(2)+9x^(2)-27x-54=0 . If alpha, beta, gamma are in geometric progression, then the value of |alpha|+|beta|+|gamma|=

Let alpha, beta and gamma are the roots of the equation 2x^(2)+9x^(2)-27x-54=0 . If alpha, beta, gamma are in geometric progression, then the value of |alpha|+|beta|+|gamma|=

Let alpha, beta and gamma be the roots of equation x^(3)+x+1=0 , then (alpha beta(alpha+beta)+betagamma(beta+gamma)+gamma alpha(gamma+alpha))/(alpha^(2)+beta^(2)+gamma^(2)) is equal to

Let alpha, beta and gamma be the roots of equation x^(3)+x+1=0 , then (alpha beta(alpha+beta)+betagamma(beta+gamma)+gamma alpha(gamma+alpha))/(alpha^(2)+beta^(2)+gamma^(2)) is equal to

If (1+alpha)/(1-alpha),(1+beta)/(1-beta), (1+gamma)/(1-gamma) are the cubic equation f(x) = 0 where alpha,beta,gamma are the roots of the cubic equation 3x^3 - 2x + 5 =0 , then the number of negative real roots of the equation f(x) = 0 is :

If (1+alpha)/(1-alpha),(1+beta)/(1-beta), (1+gamma)/(1-gamma) are the cubic equation f(x) = 0 where alpha,beta,gamma are the roots of the cubic equation 3x^3 - 2x + 5 =0 , then the number of negative real roots of the equation f(x) = 0 is :

If (1+alpha)/(1-alpha),(1+beta)/(1-beta),(1+gamma)/(1-gamma) are the cubic equation f(x)=0 where alpha,beta,gamma are the roots of the cubic equation 3x^(3)-2x+5=0 ,then the number of negative real roots of the equation f(x)=0 is :

Let alpha,beta be the roots of the equation x^(2)-(2a+1)x+a=0 and gamma,delta be the roots of the equation x^(2)+(a-4)x+a-1=0. If (alpha)/(gamma)-(delta)/(beta)=(alpha delta(alpha-gamma+beta-delta))/(a) then the value of (a-1)^(-2) is