The roots of the equation `t^3+3a t^2+3b t+c=0a r ez_1, z_2, z_3` which represent the vertices of an equilateral triangle. Then `a^2=3b` b. `b^2=a` c. `a^2=b` d. `b^2=3a`

Let z_1 and z_2 be theroots of the equation z^2+az+b=0 z being complex. Further, assume that the origin z_1 and z_2 form an equilateral triangle then (A) a^2=4b (B) a^2=b (C) a^2=2b (D) a^2=3b

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 A(z_(1)),B(z_(2)), C(z_(3)) are the vertices of an equilateral triangle ABC, then arg (2z_(1)-z_(2)-z_(3))/(z_(3)_z_(2))=

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.

If A(z_1), B(z_2). C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_2-2z_1)/(z_3-z_2))=pi/4 Reason(R): If /_B=alpha, then

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) .

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=,z_3=1-isqrt(3)

In the equation, ax^2+bx+c=0 , a,b and c in Z , if 3+i is a root of the equation, then value of a+b+c=?