If `alpha and beta` are the roots of the equation `x^2 + 5x-49=0`, then find the value of `cot(cot^-1 alpha + cot^-1 beta)`.

If alpha, beta are the roots of the equation 2x^2+5x+3=0 , then find the value of beta/alpha + alpha/beta .

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

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

If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > beta) then find the value of 1/(alpha)^2 + 1/(beta)^2

If alpha and beta are the roots of the equation x^(2)-x-4=0 , find the value of (1)/(alpha)+(1)/(beta)-alpha beta :

2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0. If cot alpha and cot beta are the roots of the equation x^(2)+ bx + c = 0" with " b != 0, " then the value of " cot(alpha + beta) is

If alpha and beta are the roots of the equation 3x^(2) - 5x + 2 = 0 , find the value of (i) (alpha)/(beta) + (beta)/(alpha) (ii) alpha-beta (iii) (alpha^(2))/(beta) + (beta^(2))/(alpha)

If alpha and beta are the roots of equation 6x^(2)+x-2=0 , find the value of (alpha)/(beta)+(beta)/(alpha) :