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 z_(1),z_(2),z_(3) are the vertices of the o+ABC on the complex plane and are also the roots of the equation z^(3)-3az^(2)+3 beta z+gamma=0 then the condition for the o+ABC to be equilateral triangle is: alpha^(2)=beta( b) alpha=beta^(2)alpha^(2)=3 beta(d)alpha=3 beta^(2)

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

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 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 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 are the roots a^(x)-2bx+c=0 then alpha^(3)beta^(3)+alpha^(2)beta^(3)+beta^(2)alpha^(3)=

The roots z_(1),z_(2),z_(3) of the equation z^(3)+3 alpha z^(2)+3 beta z+gamma=0 correspond to the points A,B and C on the complex plane.Find the complex number representing the centroid of the triangle ABC, and show that the triangle is equilateral if alpha^(2)=beta