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 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]]

Let a,b,c are the solutions of the cubic x^(3)-5x^(2)+3x-1=0, then find the value of the determinant det[[a,b,ca,b,ca-b,b-c,c-ab+c,c+a,a+b]]

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 the sum of the base 2 logarithms of the roots of the cubic f(x)=8x^(3)+4ax^(2)+2x+a=0 is 5 then the value of a'a' is -64(b)-8(c)-128(d)-256