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`

The roots of the equation t^(3)+3at^(2)+3bt+c=0 are z_(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

If A(z_1), B(z_2), C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_3-2z_1)/(z_3-z_2)) is equal to

Assertion (A) : The origin and the roots of the equation x^(2) + ax + b = 0 form an equilateral triangle if a^(2) = 3b Reason (R) : If z_(1) , z_(2) , z_(3) are vertices of an equilateral triangle then z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = z_(1) z_(2) + z_(2) z_(3) + z_(3) z_(1)

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

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))=

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 .