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`

If alpha, beta are roots of the equation ax^2 + bx + c = 0 then the equation whose roots are 2alpha + 3beta and 3alpha + 2beta is

If alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 then the coefficient of x in cubic equation whose roots are alpha ( beta + gamma ) , beta ( gamma + alpha) and gamma ( alpha + beta) is

Let alpha,beta be the roots of the equation ax^2+bx+c=0 . A root of the equation a^3x^2+abcx+c^3=0 is (i) alpha+beta (ii) alpha^2+beta (iii) alpha^2-beta (iv) alpha^2beta

Let alpha,beta be the roots of the equation ax^2+bx+c=0 . A root of the equation a^3x^2+abcx+c^3=0 is (i) alpha+beta (ii) alpha^2+beta (iii) alpha^2-beta (iv) alpha^2beta

If alpha , beta , gamma are the roots of the equation x^3 +4x^2 -5x +3=0 then sum (1)/( alpha^2 beta^2)=

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta is :

If the complex numbers z_1,z_2,z_3 represents the vertices of a triangle ABC, where z_1,z_2,z_3 are the roots of equation z^3+3alphaz^2+3alphaz^2+3betaz+gamma=0, alpha,beta,gamma beng complex numbers and alpha^2=beta then /_\ABC is (A) equilateral (B) right angled (C) isosceles but not equilateral (D) scalene

If alpha, beta and gamma are the roots of the equation x^(3)-px^(2)+qx-r=0 , then the value of alpha^(2)beta+alpha^(2)gamma+beta^(2)alpha+beta^(2)gamma+gamma^(2)alpha+gamma^(2)beta is equal to

If alpha,beta are roots of x^2-px+q=0 then find the quadratic equation whose roots are ((alpha^2-beta^2)(alpha^3-beta^3)) and alpha^2beta^3+alpha^3beta^2

If alpha, beta, gamma, are the roots of the equation x^(3)+3x-1=0, then equation whose roots are alpha^(2),beta^(2),gamma^(2) is