If `alpha` is a real root of the cubic equation `ax^3+bx^2+bx+a=0,` then the value of `lim_(x->1/alpha)tan(a x^3+b x^2+b x+a)/((alphax-1)` is

If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = 0 (b < c) , then the value of tan^-1 alpha+ tan^-1 (alpha^-1) is equal to :

If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = 0 (b < c) , then the value of tan^-1 alpha+ tan^-1 (alpha^-1) is equal to :

If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = 0 (b < c) , then the value of tan^-1 alpha+ tan^-1 (alpha^-1) is equal to :

If alpha is the only real root of the equation x^(3)+bx^(2)+cx+1=0(b

If alpha and beta be the roots of the quadratic equation ax^2+bx+c=0 then evaluate lim_(xrarralpha)(1-cos(ax^2+bx+c))/((x-alpha)^2)

If x=2 is a real root of cubic equation f (x) = 3x^(3)+bx^(2)+bx+3=0 . Then the value of lim_(xrarr(1)/(2)) (e^(f(x)-1)/(2x-1))

If alpha is the only real root of the equation x^(3) + bx^(2) + cx + 1 = 0 (b lt c) , then find the value of tan^(-1) alpha + tan^(-1) (alpha^(-1))

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+c=0, then evaluate lim_(x rarr(1)/(a))sqrt((1-cos(cx^(2)+bx+a))/(2(1-alpha x)^(2)))

If x=2 is a real root of cubic equations f(x)=3x^(3)+bx^(2)+bx+3=0 then the value of lim alue of lim_(x rarr(1)/(2))(e^(f(x))-1)/(2x-1)=