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 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 and c are the roots of the equation x^3+2x^2+1=0 , find |[a,b,c],[b,c,a],[c,a,b]| .

If a ,\ b ,\ c are roots of the equation x^3+p x+q=0 , prove that detrminant of \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{bmatrix} is zero

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

The roots of the equation ( a-b) x^2 +(b-c) x+ (c-a) =0 are

The roots of the equation (b-c)x^(2)+(c-a)x+(a-b)=0

If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove that a,b, c are in G.P,

If c, d are the roots of the equation (x-a) (x-b) - k=0 , then prove that a, b are the roots of the equation (x-c) (x-d) + k= 0