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`

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 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 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=-2,z_3=1-isqrt(3)

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot

If one root of the equation 2x^2+b x+c=0 is three times the other, then b^2: a c= (a) 3:1 (b) 3:16 (c) 16:3 (d) 16:1

If a and b are two real number lying between 0 and 1 such that z_1=a+i, z_2=1+bi and z_3=0 form an equilateral triangle , then (A) a=2+sqrt(3) (B) b=4-sqrt(3) (C) a=b=2-sqrt(3) (D) a=2,b=sqrt(3)

Let A(z_(1)),B(z_(2)),C(z_(3)) be the vertices of an equilateral triangle ABC in the Argand plane, then the number (z_(2)-z_(3))/(2z_(1)-z_(2)-z_(3)) , is

Assertion (A): z_1,z_2 and origin form an equilateral triangle if p^2=6q for the equation z^2 + pz+q=0 , Reason (R): Triangle having vertices z_1,z_2,z_3 in the Argand plane is equilateral if z_1^2+z_2^2+z_3^2=z_1z_2+z_2z_3+z3z_1 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.