I graphed the function $\displaystyle x^3-2x+3$, and it appears that there is one real root. I wanted to use the rational zero theorem to determine the root but it doesn't agree with my geometric picture. According to Wolfram, if the coefficients of the polynomial are specified to be integers then we can form rational zeros, $\displaystyle \pm{p/q}$, from the leading and terminal coefficients.

From this, I got $\displaystyle \pm3$,$\displaystyle \pm1$. But this is incorrect as none of the possible rational zeros check out.