The Radical Solution and Computational Complexity

The radical solution of polynomials with rational coefficients is a famous solved problem. This paper found that it is a NP problem. Furthermore, this paper found that arbitrary P ∈ P shall have a one-way running graph G, and have a corresponding Q ∈ NP which have a two-way running graph $G'$, G and $G'$ is isomorphic, i.e., $G'$ is combined by G and its reverse G⁻¹. When P is an algorithm for solving polynomials, G⁻¹ is the radical formula. According to Galois' Theory, a general radical formula does not exist. Therefore, there exists an NP, which does not have a general, deterministic and polynomial time-complexity algorithm, i.e., P ≠ NP. Moreover, this paper pointed out that this theorem actually is an impossible trinity.