Which of the following are roots of the polynomial function below? f(x)=x^3-3x^2+2

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