How many roots exist in the following polynomial, according to the fundamental theory of algebra?
\[
3 x^{4}-7 x^{2}+8
\]

Step 1 ：The given polynomial is \(3x^{4}-7x^{2}+8\).

Step 2 ：The fundamental theorem of algebra states that every non-constant polynomial equation has at least one root in the complex number system. The number of roots is equal to the degree of the polynomial.

Step 3 ：In this case, the degree of the polynomial is 4, so there should be 4 roots. However, these roots may be real or complex, and they may be distinct or repeated.

Step 4 ：The roots of the polynomial are \(-6^{3/4}\cos(\frac{\atan(\sqrt{47}/7)}{2})/3 - 6^{3/4}i\sin(\frac{\atan(\sqrt{47}/7)}{2})/3\), \(-6^{3/4}\cos(\frac{\atan(\sqrt{47}/7)}{2})/3 + 6^{3/4}i\sin(\frac{\atan(\sqrt{47}/7)}{2})/3\), \(6^{3/4}\cos(\frac{\atan(\sqrt{47}/7)}{2})/3 - 6^{3/4}i\sin(\frac{\atan(\sqrt{47}/7)}{2})/3\), and \(6^{3/4}\cos(\frac{\atan(\sqrt{47}/7)}{2})/3 + 6^{3/4}i\sin(\frac{\atan(\sqrt{47}/7)}{2})/3\).

Step 5 ：Final Answer: There are \(\boxed{4}\) roots in the given polynomial according to the fundamental theorem of algebra.