Solve the equation `|a-x c b c b-x a b a c-x|=0w h e r ea+b+c!=0.`

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

Solve the equation, (x - ab)/(a + b) + (x - bc)/(b + c) + (x - ca)/(c + a)= a + b + c . What happens if 1/(a + b) + 1/( b + c) + 1/(c + a) = 0

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

If a + b + c = 0 and a ne c then the roots of the equation (b + c - a)x^(2) + (c + a - b)x + (a + b - c) = 0 , are

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 the roots of the quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

Show that the roots of the quadratic equation: (b - c)x^(2) + (c - a) x + (a - b) = 0 are equal if c + a = 2b.