Show that `[[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]=0` where `alpha,beta,gamma` are in AP

Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0,where" "alpha,beta,gamma are in A.P

|[x-3, x-4, x-alpha], [x-2, x-3, x-beta], [x-1, x-2, x-gamma]| =0,"where" alpha, beta, gamma "are in AP"

If alpha,beta,gamma are in A.P. then show that , |[x-3,x-4,x-alpha],[x-2,x-3 ,x-beta],[x-1,x-2,x-gamma]|=0

If alpha,beta,gamma are the zeroes of 3x^3-5x^2-11x-3 , then alpha+beta+gamma =

If the roots of x(3-x^2)+2x^2=0 are alpha,beta,gamma then the value of alpha+beta+gamma+1 is ________ .

If alpha , beta, gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to

If the roots of 4-3x+5x^2+x^3=0 are alpha,beta,gamma then the value of 1/alpha+1/beta+1/gamma= ________ .

If alpha beta gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to

If alpha, beta, gamma are the roots of x^3+a x^2+b=0 then the value of [[alpha , beta , gamma],[beta , gamma , alpha],[gamma , alpha , beta]] is