let `|{:(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x):}|=(1)/(6)(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4))` be an identity in x, where `alpha_(1),alpha_(2),alpha_(3),alpha_(4)` are independent of x. Then find the value of `alpha_(1)alpha_(2)alpha_(3)alpha_(4)`

If |{:(1+x^(2),3x,x+1),(5,x,x^(3)),(0,1,x+2):}|=(alpha_(1)-x)(alpha_(2)-x)(alpha_(3)-x)(alpha_(4)-x)(alpha_(5)-x) is an identity, where alpha_(1),alpha_(2),alpha_(3),alpha_(4),alpha_(5) are complex numbers independent of x ,then the value of alpha_(1)*alpha_(2)*alpha_(3)*alpha_(4)*alpha_(5) 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 find the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4))

If alpha_(1),alpha_(2),alpha_(3)......alpha_(n) are roots of the equation f(x)=0 then (-alpha_(1),-alpha_(2),-alpha_(3),......alpha_(n)) are the roots of

If alpha and beta are zeroes of 5x^(2)-7x+1 , then find the value of (1)/(alpha)+(1)/(alpha) .

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_(1),alpha_(2) are the roots of x^(2)+ax+1=0andalpha_(3),alpha_(4) are the roots of x^(2)+bx+1=0 then (alpha_(1)+alpha_(3))(alpha_(2)+alpha_(3))(alpha_(1)+alpha_(2))(alpha_(2)+alpha_(4))=

If alpha_(1),alpha_(2),alpha_(3), alpha_(4) are the roos of x^(4)+2x^(3)+bx^(2)+cx+d=0 such that alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2) , then b-c is equal to__________