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 _____.

Suppose 1,2,3 are the roots of the equation x^4 + ax^2 + bx + c = 0 . Find the value of 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)

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

Let a,b,c be roots of the cubic equation x^(3)-3x^(2)-2=0. Find the value of det[[a,1,11,b,11,1,c]]

Let a,b,c be roots of the cubic equation x^(3)-3x^(2)-2=0. Find the value of det[[a,1,11,b,11,1,c]]

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 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 a, b and c be the roots of 3 x^(3)+8 x+7=0 , then the value of (a+b)^(3)+(b+c)^(3)+(c+a)^(3) is equal to