According to the fundamental theorem of algebra, how many roots exist for the polynomial function?

f(x) = (x3 – 3x + 1)2
2 roots
3 roots
6 roots
9 roots

Be careful this is tricky. X^3-3x+1 has three different roots.

Now (x^3-3x+1)^2 has three different roots but each is double!

That's where it's tricky.

3 different roots,

But indeed 6 with 3 double. Counting multiplicity. If u know whether they count multiple roots or not ...

Strictly speaking, the answer is 6 (multiplicity is considered)