The origin and the roots of the equation `z^(2)+pz+q=0` form an equilateral triangle, if

Find the roots of the equations. Q. x^(2)-2x+5=0

Find the roots of the equations. Q. 2x^(2)+x-3=0

If lambda in R such that the origin and the non-real roots of the equation 2z^(2)+2z+lambda=0 form the vertices of an equilateral triangle in the argand plane, then (1)/(lambda) is equal to

If the origin and the non - real roots of the equation 3z^(2)+3z+lambda=0, AA lambda in R are the vertices of an equilateral triangle in the argand plane, then sqrt3 times the length of the triangle is

Prove that quadrilateral formed by the complex numbers which are roots of the equation z^(4) - z^(3) + 2z^(2) - z + 1 = 0 is an equailateral trapezium.

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

The equation of a circle with the origin as the centre and passing through the vertices of an equilateral triangle whose altitude is of length 3 units is

If z is a complex number, then the area of the triangle (in sq. units) whose vertices are the roots of the equation z^(3)+iz^(2)+2i=0 is equal to (where, i^(2)=-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)