The roots `z_1, z_2, z_3` of the equation `x^3 + 3ax^2 + 3bx + c = 0` in which a, b, c are complex numbers correspond to points A, B, C. Show triangle will be an equilateral triangle if `a^2=b`.

The roots z_1,z_2,z_3 of the equation x^3+3ax^2+3bx+c=0 in which a,b,c are complex number correspond to the points A,B,C on the gaussian pllane. Find the centroid of the triangle ABC and show that it will equilateral if a^2=b

If the equation ax^2 + bx + c = 0, 0 < a < b < c, has non real complex roots z_1 and z_2 then

If the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then

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

If z_(1) and z_(2) are the roots of the equation az^(2)+bz+c=0,a,b,c in complex number and origin z_(1) and z_(2) form an equilateral triangle,then find the value of (b^(2))/(ac) .

Let z_(1)" and "z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number further, assume that the origin, z_(1)" and "z_(2) form an equilateral triangle, then

Let z_1 and z_2 be the roots of the equation 3z^2 + 3z + b=0 . If the origin, together with the points represented by z_1 and z_2 form an equilateral triangle then find the value of b.

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