If `a,b,c` are the roots of the equation `7x^3-25x+42=0` then the value of the expression `(a+b)^3+(b+c)^3+(c+a)^3` is

The expression (a-b)^3+(b-c)^3+(c-a)^3 =0 if :

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 the roots of the cubic x^(3)-x^(2)+2x-3=0, then find the absolute value of the expression (a)/(a+bc)+(b)/(b+ac)+(c)/(c+ab)

The expression (a - b)^3 + (b - c)^3 + (c - a)^3 = 0 if :

If a,b,c are the roots of the equation x^(3)+px+q=0, then find the value of the determinant |1+a1111+b1111+c|

Suppose a,b,c are the roots of the cubic x^(3)-x^(2)-2=0. Then the value of a^(3)+b^(3)+c^(3) is

If a,b,c are the roots of the equation x^(3)-3x^(2)+3x+7=0, then the value of det[[2bc-a^(2),c^(2),b^(2)c^(2),2ac-b^(2),a^(2)b^(2),a^(2),2ab-c^(2)]] is

If x=(2)/(3) and x=-3 are the roots of the equation ax^(2)+7x+b=0, find the values of a and b.