Let `ax^3+bx^2+cx+d =|(x+1,2x,3x),(2x+3,x+1,x), (2-x,3x+4,5x-1)|` then what is the value of c

Let ax^(3) + bx^(2) + cx + d |(x+1,2x,3x),(2x+3,x+1,x),(2-x,3x+4,5x-1)| , then What is the value of a + b + c + d ?

Let ax^3+bx^2+cx+d=|{:(3x,x+1,x-1),(x-3,-2x,x+2),(x+3,x-4,5x):}| then the value of d is

Let ax^3+bx^2+cx+d=|{:(3x,x+1,x-1),(x-3,-2x,x+2),(x+3,x-4,5x):}| then the value of d is

If ax^4+bx^3+cx^2+dx+e=|[2x,x-1,x+1] , [x+1, x^2-x,x-1] , [x-1,x+1,3x]| then the value of c is

Let x_1,x_2,x_3,x_4 ,be the roots (real or complex) of the equation x^4+ax^3+bx^2+cx+d=0 . If x_1+x_2=x_3+x_4 and a,b,c,d in R, then If a=2, then the value of b-c is

IF |{:(1+x,x,x^2),(x,1+x,x^2),(x^2,x,1+x):}| =a+bx+cx^2+dx^3+ex^4+fx^5 then write the value of a.

Let x_(1),x_(2),x_(3),x_(4) be the roots (real or complex) of the equation x^(4)+ax^(3)+bx^(2)+cx+d=0. If x_(1)+x_(2)=x_(3)+x_(4) and a,b,c, d in R, then find the value of b-c

If ax^(4) + bx^(3) + cx^(2) + dx + e = |{:(x^(3) + 3x , x - 1 , x+ 3) , (x + 1 , -2x , x- 4) , (x - 3 , x + 4 , 3x):}| , then e =