## Precalculus (6th Edition) Blitzer

Let $f\left( x \right)={{x}^{4}}+3{{x}^{2}}+2$ be a polynomial of degree $4$. The zeros of the polynomial are, \begin{align} & {{x}^{4}}+3{{x}^{2}}+2=0 \\ & {{x}^{4}}+2{{x}^{2}}+{{x}^{2}}+2=0 \\ & \left( {{x}^{2}}+1 \right)\left( {{x}^{2}}+2 \right)=0 \\ & x=\pm i,\pm \sqrt{2}i \end{align} All these roots are not actual rational zeros. Thus, the given statement makes sense.