The number of values of a for which equations  ${\mathrm{x}}^3+\mathrm{ax}+1=0\text{ and }{\mathrm{x}}^4+{\mathrm{ax}}^2+1=0$ have a common root is

Given equations are 
$$\begin{gathered} {\mathrm{x}}^3+\mathrm{ax}+1=0 \\ \mathrm{or} {\mathrm{x}}^4+{\mathrm{ax}}^2+\mathrm{x}=0 \left(1\right) \\ \mathrm{and} {\mathrm{x}}^4+{\mathrm{ax}}^2+1=0 \left(2\right) \end{gathered}$$
From (1) - (2), we get x = 1. Thus, x = 1 is the common roots.
Hence,
$1+\mathrm{a}+1=0\Rightarrow \mathrm{a}=-2$