Solve the equation: `|[x+a, b,c],[a,x+b,c],[a,b,x+c]|=0 `

If a+b+c=0, solve the equation: |[a-x, c, b],[c,b-x, a],[b, a, c-x]|=0

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c andb(a+c)> a c

Solve the equation |{:(x+a,c+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0

If a != b != c , are value of x which satisfies the equation |(0,x -a,x -b),(x +a,0,x -c),(x +b,x +c,0)| = 0 is given by

det[[ Solve the equation a-x,c,bc,b-x,ab,a,c-x]]=0 where a+b+c!=0

If a, b, c are the roots of the equation x^3-12x^2+39x-21=0 then find the value of the determinant |[a, b-c, c+b] , [ a+c, b, c-a] , [a-b, b+a, c]|

If a , b , c , are roots of the equation x^3+p x+q=0, prove that |[a ,b, c],[ b ,c, a],[ c, a, b]|=0

If a,b,c, in R, find the number of real root of the equation |{:(x,c,-b),(-c,x,a),(b,-a,x):}| =0

If a ne b ne c , then one value of x which satisfies the equation. [(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)] = 0 is given by :