Question 77
Let $S$ be the set of points $(a, b)$ with $0 \leq a, b \leq 1$ such that the equation
$$
x^{4}+a x^{3}-b x^{2}+a x+1=0
$$
has at least one real root. Determine the area of the graph of $S$.
$$
x^{4}+a x^{3}-b x^{2}+a x+1=0
$$
has at least one real root. Determine the area of the graph of $S$.