The roots of the cubic equation (z + `alpha` `beta`)^3 = `alpha`^3 , `alpha` is not equal to 0, represent the vertices of a triangle of sides of length

The roots of the cubic equation (z+ab)^(3)=a^(3),a!=0 represents the vertices of an equilateral triangle of sides of length

if alpha and beta are the roots of the equation 2x^(2)-5x+3=0 then alpha^(2)beta+beta^(2)alpha is equal to

If alpha,beta are roots of the equation ax^(2)-bx-c=0, then alpha^(2)-alpha beta+beta^(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 alpha and beta are the roots of the equation x^2-6x+6=0 what is alpha^3+beta^3+alpha^2+beta^2+alpha+beta equal to

If alpha and beta are the roots of the equation x^(2)+x+c=0 such that alpha+beta, alpha^(2)+beta^(2) and alpha^(3)+beta^(3) are in arithmetic progression, then c is equal to