If `z_1,z_2,z_3` are the vertices of the ` A B C` on the complex plane and are also the roots of the equation `z^3-3a z^2+3betaz+gamma=0` then the condition for the ` A B C` to be equilateral triangle is: `alpha^2=beta` (b) `alpha=beta^2` `alpha^2=3beta` (d) `alpha=3beta^2`

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

alpha and beta are the roots of the equation ax^(2)+bx+c=0 and alpha^(4) and beta^(4) are the roots of the equation lx^(2)+mx+n=0 if alpha^(3)+beta^(3)=0 then 3a,b,c

If the complex numbers z_1,z_2,z_3 represents the vertices of a triangle ABC, where z_1,z_2,z_3 are the roots of equation z^3+3alphaz^2+3alphaz^2+3betaz+gamma=0, alpha,beta,gamma beng complex numbers and alpha^2=beta then /_\ABC is (A) equilateral (B) right angled (C) isosceles but not equilateral (D) scalene

If alpha,beta are roots of the equation ax^(2)+bx+c=0 then the equation whose roots are 2 alpha+3 beta and 3 alpha+2 beta is

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

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

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 are the roots of the equation x^(2)-2x+3=0 obtain the equation whose roots are alpha^(3)-3 alpha^(2)+5 alpha-2 and beta^(3)-beta^(2)+beta+5

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