`x^3-x^2+betax+gamma=0` where `beta`and `gamma` are real .If the roots of the equation are in A.P then the mean than the mean root 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 :

If alpha, beta, gamma are the roots of the equation x^3 - 3x + 11 =0 , then alpha + beta + gamma 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 alpha, beta , gamma are the roots of the equation x^3-3x+2=0 then the equation whose roots are 1/alpha,1/beta,1/gamma is :

If alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 then the coefficient of x in cubic equation whose roots are alpha ( beta + gamma ) , beta ( gamma + alpha) and gamma ( alpha + beta) is

If alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 then the coefficient of x in cubic equation whose roots are alpha ( beta + gamma ) , beta ( gamma + alpha) and gamma ( alpha + beta) is

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

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