Let` X_1, X_2, x_3 ` be `3` roots of the cubic ` x^3 – X-1 = 0. ` Then the expression ` x_1(x_2 - X_3)^2 + x_2 (x_3 - x_1)^2 + x_3(x_1 - x_2)^2` equals a rational number.Find the absolute value of the number.

Let x_(1),x_(2), x_(3) be roots of equation x^3 + 3x + 5 = 0 . What is the value of the expression (x_(1) + 1/x_(1))(x_(2)+1/x_(2)) (x_(3)+1/x_(3)) ?

Let x_1, x_2, x_3 be the roots of equation x^3-x^2+beta x+gamma=0 . If , x_1,x_2,x_3 are in A.P. then

let x_(1),x_(2),x_(3) be the roots of equation x^(3)+3x+5=0 what is the value of the expression (x_(1)+(1)/(x_(1)))(x_(2)+(1)/(x_(2)))(x_(3)+(1)/(x_(3)))=?

The number of solutions of the equation : x_2-x_3=1 -x_1+2x_3=2 x_1-2x_2=3 is :

Let x_1 , x_2 , be the roots of the equation x^2 - 3x +p=0 and let x_3 , x_4 be the roots of the equation x^2 - 12 x + q =0 if the numbers x_1 , x_2 , x_4 ( in order ) form an increasing G.P then

Let x_(1), x_(2) be the roots of the equation x^(2)-3 x+p=0 and let x_(3), x_(4) be the roots of the equation x^(2)-12 x+q=0 . If the numbers x_(1), x_(2) x_(3), x_(4) (in order) form an increasing G.P. then,

If the roots x_(1),x_(2),x_(3) of the equation x^(3)+ax+a=0 (where a in R-{0} ) satisfy (x_(1)^(2))/(x_(2))+(x_(2)^(2))/(x_(3))+(x_(3)^(2))/(x_(1))=-8 , then find the value of a and the roots of the given cubic equation.

If the roots x_(1),x_(2),x_(3) of the equation x^(3)+ax+a=0 (where a in R-{0} ) satisfy (x_(1)^(2))/(x_(2))+(x_(2)^(2))/(x_(3))+(x_(3)^(2))/(x_(1))=-8 , then find the value of a and the roots of the given cubic equation.