If `x^3 - x^2 + tan^2 alpha x - tan^2 alpha = 0,` has positive roots `X_1, X_2, X_3,` then which of following are true?

The equation alpha x^(3)-2(alpha+1) x^(2)+4 alpha x=0 has real roots and alpha is any positive integer, then the sum of the roots of the equation is

If -1,2 and alpha are the roots of 2x^3 +x^2-7x-6=0 , then find alpha

If -1,2 and alpha are the roots of 2x^3 +x^2-7x-6=0 , then find alpha

if (1+k)tan^(2)x-4tan x-1+k=0 has real roots tan x_(1) and tan x_(2) then

If alpha, beta and 1 are the roots of x^3-2x^2-5x+6=0 , then find alpha and beta

If alpha, beta and 1 are the roots of x^3-2x^2-5x+6=0 , then find alpha and beta

Let alpha in (0, pi/2) be fixed. If the integral int(tan x + tan alpha)/(tan x - tan alpha)dx = A(x)cos 2 alpha+B(x) sin 2 alpha +C ,where C is a constant of integration, then the functions A(x) and B(x) are respectively.

Let alpha in (0, pi//2) be fixed. If the integral int("tan x" + "tan" alpha)/("tan x" - "tan" alpha)dx = A(x)"cos 2 alpha+B(x) "sin" 2 alpha +C ,where C is a constant of integration, then the functions A(x) and B(x) are respectively.