Answer:
roots are {1-√3, 1, 1+√3}
Step-by-step explanation:
The sum of coefficients is 0, so you know x=1 is a root. Dividing the polynomial by (x-1) gives (x² -2x -2) as the quotient. By completing the square or using the quadratic formula, you can find the roots of that to be 1±√3.
f(x) = (x -1)(x² -2x -2)
... x = 1 is a root
The roots of x² -2x -2 are the other two roots.
... x² -2x -2 = (x² -2x +1) -3 = (x -1)² -3
... This will be zero when ...
... (x -1)² = 3
... x -1 = ±√3
... x = 1 ±√3 . . . . the other two roots
