If `alpha_1, alpha_2, alpha_3, alpha_4` are the roots of the equation `x^4+(2-sqrt3)x^2+2+sqrt3=0` then find the value of `(1-alpha_1)(1-alpha_2)(1-alpha_3)(1-alpha_4)`

If alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 then find the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4))

If alpha_(1), alpha_(2), alpha_(3), alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 , then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4)) is

If alpha_(1), alpha_(2), alpha_(3), alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 , then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4)) is :

If alpha_(1) , alpha_(2) , alpha_(3) , alpha_(4) are the roots of the equation 3x^(4)-(l+m)x^(3)+2x+5l=0 and sum alpha_(1)=3 , alpha_(1)alpha_(2)alpha_(3)alpha_(4)=10 then (l,m)

If alpha,beta are the roots of the equation 3x^(2)-6x+4=0 , find the value of ((alpha)/(beta)+(beta)/(alpha))+2((1)/(alpha)+(1)/(beta))+3alphabeta .

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_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_1-alpha_2)(alpha_1-alpha_3)(alpha_1-alpha_n)=n(alpha_1^ n-1+a)

If alpha_1,alpha_2,alpha_3,alpha_4 be the roots of x^5-1 =0 then prove that (w-alpha_1)/(w^2-alpha_1).(w-alpha_2)/(w^2-alpha_2).(w-alpha_3)/(w^2-alpha_3).(w-alpha_4)/(w^2-alpha_4)=w where w is a nonreal complex cube root of unity.