<s>[INST] The sum of non real roots of the polynomial equation $x^3+3x^2+3x+3=0$ Problem : 
The sum of non real roots of the polynomial equation $x^3+3x^2+3x+3=0$ 
(a) equals 0 
(b) lies between 0 and 1 
(c)lies between -1 and 0  
(d) has absolute value bigger than 1 
My approach : 
The discriminant of cubic equation $ax^3+bx^2+cx+d=0$ is given by 
$\Delta = 18abcd -4b^3d +b^2c^2 -4ac^3 -27a^2d^2$
$\Delta = -108 < 0 $ Therefore the equation has one real and two non real roots. 
But how to find the roots of this equation not getting any idea please help . thanks 
 [/INST] Hint: The equation can be written as 
$$(x+1)^3=-2.$$
Hence the three roots are $\sqrt[3]2-1$, $\sqrt[3]2\omega-1$, $-\sqrt[3]2\omega-1$, where $\omega$ is a cubic root of unit.
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