If `A=|(a, b, c), (c, a, b), (b, c, a)|` and `a, b, c` are roots of equation `x^(3)+x^(2)-4=0,` then `A A^(T)` is equal to

The roots of the equation (b-c)x^(2)+(c-a)x+(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+c=0, a,b,c in Q then roots of the equation (b+c-a) x ^(2) + (c+a-c) =0 are:

If the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are equal then

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 real and a!=b, then the roots ofthe equation,2(a-b)x^(2)-11(a+b+c)x-3(a-b)=0 are :

If a,b, cinR , show that roots of the equation (a-b)x^(2)+(b+c-a)x-c=0 are real and unequal,

If a,b,c,d in R-{0} , such that a,b are the roots of equation x^(2)+cx+d=0 and c,d are the roots of equation x^(2)+ax+b=0, then |a|+|b|+|c|+|d| is equal to