  We present six Theorems on the univariate real Polynomial, using which we
develop a new algorithm for deciding the existence of atleast one real root for
univariate integer Polynomials. Our algorithm outputs that no positive real
root exists, if and only if, the given Polynomial is a factor of a real
Polynomial with positive coefficients. Next, we define a transformation that
transforms any instance of 3-SAT into a multivariate real Polynomial with
positive coefficients, if and only if, the instance is not satisfiable.
