Final answer:
The polynomial y = x^3 - 6x^2 + 30 has exactly three roots according to the fundamental theorem of algebra, which are potentially a combination of real and complex roots.
Step-by-step explanation:
In order to determine the number of roots the polynomial y = x^3 - 6x^2 + 30 has, we can use the fundamental theorem of algebra. This theorem states that every nonconstant polynomial equation of degree n has exactly n roots in the complex number system. Since our given polynomial is cubic, which means it is of degree 3, it must have exactly 3 roots in the complex plane.
These roots could be real or complex. To check if the roots are real, one might use the discriminant or attempt to factor the polynomial if possible. However, without further analysis or graphing, we cannot determine the nature of these roots, only their quantity.