Question

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

Answer 1

f(x) = (x^3 − 3x + 1)^2 is a degree 6 polynomial (cubic squared). By the Fundamental Theorem of Algebra it has 6 complex roots counting multiplicity.

(There are 3 distinct roots of the cubic, each with multiplicity 2.)