[|x+aquad a^(2)quad a^(3)],[x+bquad b^(2)quad b^(3)],[x+cquad c^(2)quad c^(3)]|=0" and "a!=b!=c

FInd x when det[[x+a,a^(2),a^(3)x+b,b^(2),b^(3)x+c,c^(2),c^(3)]]=0 where a,b,c are distinct numbers and a!=b!=c

Solve the system of equations : z+ay+a^(2)x+a^(3)=0z+by+b^(2)x+b^(3)=0z+cy+c^(2)x+c^(3)=0] where a!=b!=c

Using properties of determinant, find the value of x: |{:(x+a, a^(2), a^(3)), (x+b, b^(2), b^(3)), (x+c, c^(2), c^(3)):}|=0

If a,b,c are distinct,then the value of x0quad x^(2)-aquad x^(3)-b satisfying det[[0,x^(2)-a,x^(3)-bx^(2)+a,0,x^(2)+cx^(4)+b,x-c,0]]=0 is c (b) a (c) b(d)0

If a, b, c are different, then value of x satisfying the equation |{:( 0 , x^(2) - a , x^(3) - b) , (x^(2) + a , 0 , x^(2) + c), (x^(4) + b , x- c , 0):}|=0 is

If (x^(2)+2x+3)/x^(3)=A/x+B/x^(2)+C/x^(3), " then " A+B-C=

If b+c = 2x, c+a =2y and a +b =2z then value of a^(3) +b^(3) +c^(3) is