= Solution
{c}
At a constant <steady state> $N_t=N$, the discrete equation reduces to
$$
N\left[\frac r{1+bN^2}-(\delta+1)\right]=0.
$$
Write $s=\delta+1>1$. For $r<s$, no nonzero real root is possible, so \b[zero is the only real steady state]. For $r>s$ the real roots are
$$
\boxed{N=0,\qquad N=\pm\sqrt{\frac{r-s}{bs}}.}
$$
Thus there is \b[exactly one strictly positive steady state], $N^*=\sqrt{(r-s)/(bs)}$. There are three real steady states in total, two of them nonnegative. At $r=s$ the only one is zero. This distinction keeps the positive-population statement separate from the count over all real numbers.
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