If `alpha,beta,gamma,delta` be first 4 positive solutions of `sinx=(sqrt3)/2` with `alpha < beta < gamma < delta` then the value of `4 sin alpha/2+(3cos)beta/2+(2sin)gamma/2+secdelta/2= ? `

If alpha,beta,gamma are the 3 positive roots of cubic x^(3)-ax^(2)+bx-16sqrt(6)=0 then the x^(3)-ax^(2)+bx-16sqrt(6)=0 then the minimum value of ((4)/(alpha beta)+(3)/(beta gamma)+(2)/(alpha gamma)) is

If alpha,beta,gamma are the 3 positive roots of cubic x^(3)-ax^(2)+bx-16sqrt(6)=0 then the x^(3)-ax^(2)+bx-16sqrt(6)=0 then the minimum value of ((4)/(alpha beta)+(3)/(beta gamma)+(2)/(alpha gamma)) is

If alpha, beta, gamma, delta are the solutions of the equation tan(theta + (pi)/(4)) = 3 tan 3 theta , no two of which have equal tangents. The value of tan alpha + tan beta + tan gamma + tan delta is

If alpha and beta are the solution of sinx=-(1)/(2) in [0, 2pi] and alpha and gamma are the solutions of cos x=-(sqrt3)/(2) in [0, 2pi] , then the value of (alpha+beta)/(|beta-gamma|) is equal to

If alpha and beta are the solution of sinx=-(1)/(2) in [0, 2pi] and alpha and gamma are the solutions of cos x=-(sqrt3)/(2) in [0, 2pi] , then the value of (alpha+beta)/(|beta-gamma|) is equal to

If alpha, beta, gamma, delta are roots of x^(4) + px^(3) + qx^(2) + rx + s = 0 then sum alpha^(2) beta gamma =

If alpha, beta, gamma, delta are roots of x^(4) + px^(3) + qx^(2) + rx + s = 0 then sum alpha^(2) beta gamma =

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is: