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 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

If A(z_1),B(z_2),C(z_3) and D(z_4) be the vertices of the square ABCD then

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

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

Let alpha,beta be the roots of the quadratic equation a x^2+b x+c=0 and delta=b^2-4a cdot If alpha+beta,alpha^2+beta^2alpha^3+beta^3 are in G.P. Then a. =0 b. !=0 c. b =0 d. c =0

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to a. 1 b. 3 c. 5 d. 7

Show that straight lines (A^2-3B^2)x^2+8A Bx y+(B^2-3A^2)y^2=0 form with the line A x+B y+C=0 an equilateral triangle of area (C^2)/(sqrt(3)(A^2+B^2)) .

Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 are equal if either b=0 or , a^3+b^3+c^3-3abc=0

If the area of the triangle formed by the points (2a ,b)(a+b ,2b+a), and (2b ,2a) is 2qdotu n i t s , then the area of the triangle whose vertices are (a+b ,a-b),(3b-a ,b+3a), and (3a-b ,3b-a) will be_____

If xsina+ysin2a+zsin3a=sin4a , xsinb+ysin2b+zsin3b=sin4b , xsinc+ysin2c+zsin3c=sin4c , then the roots of the equation t^3-(z/2)t^2-((y+2)/4)t+((z-x)/8)=0,a , b , c ,!=npi, are (a) sina ,sinb ,sinc (b) cosa ,cosb ,cosc (c) sin2a ,sin2b ,sin2c (d) cos2a ,cos2bcos2c