find x of x^3+x-2=0

Question

help please?

Answer 1

1+1-2=0 so x=1 is a root. Divide by this root using synthetic division to get a quadratic:

x³+x-2=0⇒x³+0x²+x-2=0

1 | 1 0 1 | -2

     1 1 1 |  2

     1 1 2 |  0 = x²+x+2, x=(-1±√(1-8))/2 (quadratic formula),

Complex zeroes: x=(-1+i√7)/2 and (-1-i√7)/2 (where i= √-1).

So there is only one real root x=1 and two complex conjugates.