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`

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

If alpha,beta,gamma are in A.P. show that cot beta=(sin alpha-sin gamma)/(cos gamma-cos alpha)

If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha , and gamma+alpha-beta .

If alpha,beta,gamma are the roots of the equation x^3+x+1=0 , then the value of alpha^3+beta^3+gamma^3 is.

If alpha,beta,gamma "are in A.P. show that" cot beta = (sin alpha - sin gamma)/(cos gamma -cos alpha)

If alpha,beta,gamma are the roots of x^3+ax+b =0, then the value of alpha^3+beta^3+gamma^3

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation x^3=1,t h e n \ |[a,b,c],[b,c,a],[c,a,b]| is equal to

Let alpha,beta,gamma be the roots of f(x)=0, where f(x)=x^3+x^2-5x-1 . Then [alpha]+[beta]+[gamma] is, where [.] is greatest integer function

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled