Let \(\zeta(s)\) be the Riemann zeta function. Let \(\xi(s)=\frac{1}{2}s(s-1)\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)\) be the completed zeta function. It is well known that \[\xi(s)=\sum_{j=0}^\infty \frac{\gamma(j)}{j!} z^{2j},\] where \(\gamma(n)>0\) for all \(n\geq0\). For \(d, n \geq 0\), the degree \(d\) Jensen polynomial is defined by \(J^{d,n}(X)=\sum_{j=0}^{d} \binom{d}{j}\gamma(n+j)X^j\). A polynomial with real coefficients is hyperbolic if all of its zeros are real. G. Pólya [Meddelelser København 7, Nr. 17, 33 S. (1926; JFM 52.0336.01)] showed that the Riemann hypothesis (RH) is equivalent to the hyperbolicity of \(J^{d,n}(X)\) for all \(d, n \geq 0\). In this direction, it was proved that for all \(d\geq 1\), there is a non-effective \(N(d)>0\) such that if \(n\geq N(d)\), then \(J^{d,n}(X)\) is hyperbolic. In this paper, the authors provide an effective upper bound for \(N(d)\) as follows: There is a constant \(c > 0\) such that if \(n>ce^d\), then \(J^{d,n}(X)\) is hyperbolic. As consequence, they also showed that if \(d\leq 9\times 10^{24}\) and \(n\geq 0\), then \(J^{d,n}(X)\) is hyperbolic.