Home
Class 12
MATHS
The roots z1, z2, z3 of the equation x^3...

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`.

Promotional Banner

Similar Questions

Explore conceptually related problems

If the roots of the equation x^(3) + ax^(2) + bx + c = 0 are in A.P., 2a^(3) - 9ab =

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, then

If the equation x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:b:c is

If the equations : x^(2) + 2x + 3 = 0 and ax^(2) + bx + c =0 a, b,c in R, Have a common root, then a: b : c is :

If the equation : x^(2 ) + 2x +3=0 and ax^(2) +bx+ c=0 a,b,c in R have a common root then a: b: c is :

If a+b+c=0 , then the equation 3ax^(2)+2bx+c=0 has :

Let z_(1) and z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number, assume that the origin z_(1) and z_(2) form an equilateral triangle , then

The three vertices of a triangle are represented by the complex numbers 0 , z_(1) and z_(2) . If the triangle is equilateral , then :

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.