The origin and the roots of the equation `z^2 + pz + q = 0` form an equilateral triangle If -

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 the origin and the roots of the equation z^2 + az + b=0 forms an equilateral triangle then show that the area of the triangle is (sqrt3)/(4) b.

If z_1 and z_2 are the roots of the equation z^2+az+12=0 and z_1 , z_2 forms an equilateral triangle with origin. Find absa

Let z_1,z_2 be the roots of the equation z^2+az+12=0 and z_1, z_2 form an equilateral triangle with origin. Then, the value of absa is ________ .

Let z_(1),z_(2) be the roots of the equation z^(2)+az+12=0 and z_(1),z_(2) form an equilateral triangle with origin. Then the value of |a| is

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 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

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.