Chapter 12, Problem 38P

The potential energy as a function of position for a particle is given by

$U\left(x\right)=U_0\left(\frac{x^3}{x_0{}^3}+a\frac{x^2}{x_0{}^2}+4\frac{x}{x_0}\right)$

where x₀ and a are constants. For what values of a will there be two static equilibria? Comment on the stability of these equilibria.